Econometrics and economic statistics Books

Book SynopsisCounty and City Extra: Special Decennial Census Edition is an essential single-volume source for Census 2020 information. This edition contains easy-to-read geographic summaries of the United States population by race, Hispanic origin, and housing status. It provides the most up-to-date census data for each state, county, metropolitan area, congressional district, and all cities with a population of 25,000 or more. It complements the popular and trusted County and City Extra: Annual Metro, City, and County Data Book, also published by Bernan Press.Features of this publication include:Census data on all states, counties, metropolitan areas, and congressional districts, as well as on cities and towns with populations above 25,000Key data on over 5,000 geographic areasRanking tables which present each geography type by various subjects Data from previous censuses for comparative purposes Color maps that help the user understand the data

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Book SynopsisWhen you want only one source of information about your city or county, turn to County and City Extra.This trusted reference compiles information from many sources to provide all the key demographic and economic data for every state, county, metropolitan area, congressional district, and for all cities in the United States with a 2010 population of 25,000 or more. In one volume, you can conveniently find data from 1990 to 2021 in easy-to-read tables. The annual updating of County and City Extra for 30 years ensures its stature as a reliable and authoritative source for information. No other resource compiles this amount of detailed information into one place.Subjects covered in County and City Extra include: Population by age and race Government finances Income and poverty Manufacturing, trade, and services Crime Housing Education Immigration and migration Labor force and employment

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Book SynopsisThis book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.Trade Review“‘This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. … It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.’ … The book can be recommended to all readers, who are interested in this field.” (Ludwig Paditz, zbMath 1414.62001, 2019)“This book is a rigorous, mathematically clear and self-contained and quite complete text on time series analysis, suitable both for graduate courses and as a reference book for researchers and users of stochastic temporal models.” (Nazaré Mendes Lopes, Mathematical Reviews, December, 2018)“Beran (Univ. of Konstanz, Germany) presents the mathematical foundations of time series analysis at a level suitable for advanced graduate students and researchers in statistics. The presentation is extremely concise … . the book gives definitions, theorems, and proofs, along with a few exercises and solutions. … it may be useful to graduate students and researchers as a reference.” (B. Borchers, Choice, Vol. 56 (03), November, 2018)​Table of Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 What is a time series? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Time series versus iid data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Typical assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Fundamental properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Ergodic property with a constant limit . . . . . . . . . . . . . . . . . . . 52.1.2 Strict Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Weak Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 Weak stationarity and Hilbert spaces . . . . . . . . . . . . . . . . . . . . 92.1.5 Ergodic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.6 Sufficient conditions for the a.s. ergodic property with a constant limit. . . . . . . . . . . 262.1.7 Sufficient conditions for the L2-ergodic property with a constant limit . .. . . . .. . . 272.2 Specific assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.1 Gaussian processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.2 Linear processes in L2(Ω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.3 Linear processes with E(X2t ) = ∞ . . . . . . . . . . . . . . . . . . . . . . 342.2.4 Multivariate linear processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.5 Invertibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2.6 Restrictions on the dependence structure . . . . . . . . . . . . . . . . . 493 Defining probability measures for time series . . . . . . . . . . . . . . . . . . . . . . 553.1 Finite dimensional distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2 Transformations and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Conditions on the expected value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Conditions on the autocovariance function . . . . . . . . . . . . . . . . . . . . . . 583.4.1 Positive semidefinite functions . . . . . . . . . . . . . . . . . . . . . . . . . 593.4.2 Spectral distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.3 Calculation and properties of F and f . . . . . . . . . . . . . . . . .4 Spectral representation of univariate time series . . . . . . . . . . . . . . . . . . . 814.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 Harmonic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.3 Extension to general processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.1 Stochastic integrals with respect to Z . . . . . . . . . . . . . . . . . . . . 844.3.2 Existence and definition of Z . . . . . . . . . . . . . . . . . . . . . . . . . . 894.3.3 Interpretation of the spectral representation . . . . . . . . . . . . . . 974.4 Further properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4.1 Relationship between ReZ and ImZ . . . . . . . . . . . . . . . . . . . . 984.4.2 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.3 Overtones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.4 Why are frequencies restricted to the range [-π,π]? . . . . . . . 1004.5 Linear filters and the spectral representation . . . . . . . . . . . . . . . . . . . . 1034.5.1 Effect on the spectral representation . . . . . . . . . . . . . . . . . . . . . 1034.5.2 Elimination of Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . 1075 Spectral representation of real valued vector time series . . . . . . . . . . . . 1095.1 Cross-spectrum and spectral representation . . . . . . . . . . . . . . . . . . . . . 1095.2 Coherence and phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166 Univariate ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 Stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.3 Causal stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.4 Causal invertible stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.5 Autocovariances of ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.1 Calculation by integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.2 Calculation using the autocovariance generating function . . . 1356.5.3 Calculation using the Wold representation . . . . . . . . . . . . . . . 1386.5.4 Recursive calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.5.5 Asymptotic decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.6 Integrated, seasonal and fractional ARMA and ARIMA processes . . 1476.6.1 Integrated processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.2 Seasonal ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.3 Fractional ARIMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.7 Unit roots, spurious correlation, cointegration . . . . . . . . . . . . . . . . . . . 1597 Generalized autoregressive processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.1 Definition of generalized autoregressive processes . . . . . . . . . . . . . . . 1637.2 Stationary solution of generalized autoregressive equations . . . . . . . . 1647.3 Definition of VARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.4 Stationary solution of VARMA equations . . . . . . . . . . . . . . . . . . . . . . 1697.5 Definition of GARCH processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.6 Stationary solution of GARCH equations . . . . . . . . . . . . . . . . . . . . . . . 1727.7 Definition of ARCH(∞) processes . . . . . . . . . . . . . . . . . . . . .7.8 Stationary solution of ARCH(∞) equations . . . . . . . . . . . . . . . . . . . . . 1778 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.1 Best linear prediction given an infinite past . . . . . . . . . . . . . . . . . . . . . 1818.2 Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1828.3 Construction of the Wold decomposition from f . . . . . . . . . . . . . . . . . 1878.4 Best linear prediction given a finite past . . . . . . . . . . . . . . . . . . . . . . . . 1909 Inference for µ, γ and F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.1 Location estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.3 Nonparametric estimation of γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.4 Nonparametric estimation of f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110 Parametric estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710.1 Gaussian and quasi maximum likelihood estimation . . . . . . . . . . . . . . 22710.2 Whittle approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22910.3 Autoregressive approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23210.4 Model choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

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Book SynopsisNon-extensive Entropy Econometrics for Low Frequency Series provides a new and robust power-law-based, non-extensive entropy econometrics approach to the economic modelling of ill-behaved inverse problems. Particular attention is paid to national account-based general equilibrium models known for their relative complexity.In theoretical terms, the approach generalizes Gibbs-Shannon-Golan entropy models, which are useful for describing ergodic phenomena. In essence, this entropy econometrics approach constitutes a junction of two distinct concepts: Jayne’s maximum entropy principle and the Bayesian generalized method of moments. Rival econometric techniques are not conceptually adapted to solving complex inverse problems or are seriously limited when it comes to practical implementation. Recent literature showed that amplitude and frequency of macroeconomic fluctuations do not substantially diverge from many other extreme events, natural or human-related, once they are explained in the same time (or space) scale. Non-extensive entropy is a precious device for econometric modelling even in the case of low frequency series, since outputs evolving within the Gaussian attractor correspond to the Tsallis entropy limiting case of Tsallis q-parameter around unity. This book introduces a sub-discipline called Non-extensive Entropy Econometrics or, using a recent expression, Superstar Generalised Econometrics. It demonstrates, using national accounts-based models, that this approach facilitates solving nonlinear, complex inverse problems, previously considered intractable, such as the constant elasticity of substitution class of functions. This new proposed approach could extend the frontier of theoretical and applied econometrics.

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Book Synopsis

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Book Synopsis

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Book SynopsisThis text disputes the laissez-faire direction of both economic theory and practice that has gained prominence since the mid-1970s. Dissenting voices, the author argues, have been drowned out by a sea of circular arguments and complex mathematical models that ignore real-world conditions.

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Book SynopsisVolume 32 of the NBER Macroeconomics Annual features six theoretical and empirical studies of important issues in contemporary macroeconomics, and a keynote address by former IMF chief economist Olivier Blanchard. In one study, SeHyoun Ahn, Greg Kaplan, Benjamin Moll, Thomas Winberry, and Christian Wolf examine the dynamics of consumption expenditures in non-representative-agent macroeconomic models. In another, John Cochrane asks which macro models most naturally explain the post-financial-crisis macroeconomic environment, which is characterized by the co-existence of low and nonvolatile inflation rates, near-zero short-term interest rates, and an explosion in monetary aggregates. Manuel Adelino, Antoinette Schoar, and Felipe Severino examine the causes of the lending boom that precipitated the recent U.S. financial crisis and Great Recession. Steven Durlauf and Ananth Seshadri investigate whether increases in income inequality cause lower levels of economic mobility and opportunity. Charles Manski explores the formation of expectations, considering the efficacy of directly measuring beliefs through surveys as an alternative to making the assumption of rational expectations. In the final research paper, Efraim Benmelech and Nittai Bergman analyze the sharp declines in debt issuance and the evaporation of market liquidity that coincide with most financial crises. Blanchard's keynote address discusses which distortions are central to understanding short-run macroeconomic fluctuations.

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Book SynopsisDemographic studies help make sense of key aspects of the economy, offering insight into trends in fertility, mortality, immigration, and labor force participation, as well as age, gender, and race-specific trends in health and disability. This book explores the connections between demography and economics.

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Book SynopsisThis groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework.Table of ContentsPreface xiii Acknowledgments xv About the Authors xvii Chapter 1 Concepts of Probability 1 1.1 Introduction 1 1.2 Basic Concepts 2 1.3 Discrete Probability Distributions 2 1.3.1 Bernoulli Distribution 3 1.3.2 Binomial Distribution 3 1.3.3 Poisson Distribution 4 1.4 Continuous Probability Distributions 5 1.4.1 Probability Distribution Function, Probability Density Function, and Cumulative Distribution Function 5 1.4.2 The Normal Distribution 8 1.4.3 Exponential Distribution 10 1.4.4 Student’s t-distribution 11 1.4.5 Extreme Value Distribution 12 1.4.6 Generalized Extreme Value Distribution 12 1.5 Statistical Moments and Quantiles 13 1.5.1 Location 13 1.5.2 Dispersion 13 1.5.3 Asymmetry 13 1.5.4 Concentration in Tails 14 1.5.5 Statistical Moments 14 1.5.6 Quantiles 16 1.5.7 Sample Moments 16 1.6 Joint Probability Distributions 17 1.6.1 Conditional Probability 18 1.6.2 Definition of Joint Probability Distributions 19 1.6.3 Marginal Distributions 19 1.6.4 Dependence of Random Variables 20 1.6.5 Covariance and Correlation 20 1.6.6 Multivariate Normal Distribution 21 1.6.7 Elliptical Distributions 23 1.6.8 Copula Functions 25 1.7 Probabilistic Inequalities 30 1.7.1 Chebyshev’s Inequality 30 1.7.2 Fréchet-Hoeffding Inequality 31 1.8 Summary 32 Chapter 2 Optimization 35 2.1 Introduction 35 2.2 Unconstrained Optimization 36 2.2.1 Minima and Maxima of a Differentiable Function 37 2.2.2 Convex Functions 40 2.2.3 Quasiconvex Functions 46 2.3 Constrained Optimization 48 2.3.1 Lagrange Multipliers 49 2.3.2 Convex Programming 52 2.3.3 Linear Programming 55 2.3.4 Quadratic Programming 57 2.4 Summary 58 Chapter 3 Probability Metrics 61 3.1 Introduction 61 3.2 Measuring Distances: The Discrete Case 62 3.2.1 Sets of Characteristics 63 3.2.2 Distribution Functions 64 3.2.3 Joint Distribution 68 3.3 Primary, Simple, and Compound Metrics 72 3.3.1 Axiomatic Construction 73 3.3.2 Primary Metrics 74 3.3.3 Simple Metrics 75 3.3.4 Compound Metrics 84 3.3.5 Minimal and Maximal Metrics 86 3.4 Summary 90 3.5 Technical Appendix 90 3.5.1 Remarks on the Axiomatic Construction of Probability Metrics 91 3.5.2 Examples of Probability Distances 94 3.5.3 Minimal and Maximal Distances 99 Chapter 4 Ideal Probability Metrics 103 4.1 Introduction 103 4.2 The Classical Central Limit Theorem 105 4.2.1 The Binomial Approximation to the Normal Distribution 105 4.2.2 The General Case 112 4.2.3 Estimating the Distance from the Limit Distribution 118 4.3 The Generalized Central Limit Theorem 120 4.3.1 Stable Distributions 120 4.3.2 Modeling Financial Assets with Stable Distributions 122 4.4 Construction of Ideal Probability Metrics 124 4.4.1 Definition 125 4.4.2 Examples 126 4.5 Summary 131 4.6 Technical Appendix 131 4.6.1 The CLT Conditions 131 4.6.2 Remarks on Ideal Metrics 133 Chapter 5 Choice under Uncertainty 139 5.1 Introduction 139 5.2 Expected Utility Theory 141 5.2.1 St. Petersburg Paradox 141 5.2.2 The von Neumann–Morgenstern Expected Utility Theory 143 5.2.3 Types of Utility Functions 145 5.3 Stochastic Dominance 147 5.3.1 First-Order Stochastic Dominance 148 5.3.2 Second-Order Stochastic Dominance 149 5.3.3 Rothschild-Stiglitz Stochastic Dominance 150 5.3.4 Third-Order Stochastic Dominance 152 5.3.5 Efficient Sets and the Portfolio Choice Problem 154 5.3.6 Return versus Payoff 154 5.4 Probability Metrics and Stochastic Dominance 157 5.5 Summary 161 5.6 Technical Appendix 161 5.6.1 The Axioms of Choice 161 5.6.2 Stochastic Dominance Relations of Order n 163 5.6.3 Return versus Payoff and Stochastic Dominance 164 5.6.4 Other Stochastic Dominance Relations 166 Chapter 6 Risk and Uncertainty 171 6.1 Introduction 171 6.2 Measures of Dispersion 174 6.2.1 Standard Deviation 174 6.2.2 Mean Absolute Deviation 176 6.2.3 Semistandard Deviation 177 6.2.4 Axiomatic Description 178 6.2.5 Deviation Measures 179 6.3 Probability Metrics and Dispersion Measures 180 6.4 Measures of Risk 181 6.4.1 Value-at-Risk 182 6.4.2 Computing Portfolio VaR in Practice 186 6.4.3 Backtesting of VaR 192 6.4.4 Coherent Risk Measures 194 6.5 Risk Measures and Dispersion Measures 198 6.6 Risk Measures and Stochastic Orders 199 6.7 Summary 200 6.8 Technical Appendix 201 6.8.1 Convex Risk Measures 201 6.8.2 Probability Metrics and Deviation Measures 202 Chapter 7 Average Value-at-Risk 207 7.1 Introduction 207 7.2 Average Value-at-Risk 208 7.3 AVaR Estimation from a Sample 214 7.4 Computing Portfolio AVaR in Practice 216 7.4.1 The Multivariate Normal Assumption 216 7.4.2 The Historical Method 217 7.4.3 The Hybrid Method 217 7.4.4 The Monte Carlo Method 218 7.5 Backtesting of AVaR 220 7.6 Spectral Risk Measures 222 7.7 Risk Measures and Probability Metrics 224 7.8 Summary 227 7.9 Technical Appendix 227 7.9.1 Characteristics of Conditional Loss Distributions 228 7.9.2 Higher-Order AVaR 230 7.9.3 The Minimization Formula for AVaR 232 7.9.4 AVaR for Stable Distributions 235 7.9.5 ETL versus AVaR 236 7.9.6 Remarks on Spectral Risk Measures 241 Chapter 8 Optimal Portfolios 245 8.1 Introduction 245 8.2 Mean-Variance Analysis 247 8.2.1 Mean-Variance Optimization Problems 247 8.2.2 The Mean-Variance Efficient Frontier 251 8.2.3 Mean-Variance Analysis and SSD 254 8.2.4 Adding a Risk-Free Asset 256 8.3 Mean-Risk Analysis 258 8.3.1 Mean-Risk Optimization Problems 259 8.3.2 The Mean-Risk Efficient Frontier 262 8.3.3 Mean-Risk Analysis and SSD 266 8.3.4 Risk versus Dispersion Measures 267 8.4 Summary 274 8.5 Technical Appendix 274 8.5.1 Types of Constraints 274 8.5.2 Quadratic Approximations to Utility Functions 276 8.5.3 Solving Mean-Variance Problems in Practice 278 8.5.4 Solving Mean-Risk Problems in Practice 279 8.5.5 Reward-Risk Analysis 281 Chapter 9 Benchmark Tracking Problems 287 9.1 Introduction 287 9.2 The Tracking Error Problem 288 9.3 Relation to Probability Metrics 292 9.4 Examples of r.d. Metrics 296 9.5 Numerical Example 300 9.6 Summary 304 9.7 Technical Appendix 304 9.7.1 Deviation Measures and r.d. Metrics 305 9.7.2 Remarks on the Axioms 305 9.7.3 Minimal r.d. Metrics 307 9.7.4 Limit Cases of L∗p(X, Y) and Θ∗p(X, Y) 310 9.7.5 Computing r.d. Metrics in Practice 311 Chapter 10 Performance Measures 317 10.1 Introduction 317 10.2 Reward-to-Risk Ratios 318 10.2.1 RR Ratios and the Efficient Portfolios 320 10.2.2 Limitations in the Application of Reward-to-Risk Ratios 324 10.2.3 The STARR 325 10.2.4 The Sortino Ratio 329 10.2.5 The Sortino-Satchell Ratio 330 10.2.6 A One-Sided Variability Ratio 331 10.2.7 The Rachev Ratio 332 10.3 Reward-to-Variability Ratios 333 10.3.1 RV Ratios and the Efficient Portfolios 335 10.3.2 The Sharpe Ratio 337 10.3.3 The Capital Market Line and the Sharpe Ratio 340 10.4 Summary 343 10.5 Technical Appendix 343 10.5.1 Extensions of STARR 343 10.5.2 Quasiconcave Performance Measures 345 10.5.3 The Capital Market Line and Quasiconcave Ratios 353 10.5.4 Nonquasiconcave Performance Measures 356 10.5.5 Probability Metrics and Performance Measures 357 Index 361

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Book SynopsisAutoregressive Conditional Heteroskedastic (ARCH) processes are used in finance to model asset price volatility over time. This book introduces both the theory and applications of ARCH models and provides the basic theoretical and empirical background, before proceeding to more advanced issues and applications. The Authors provide coverage of the recent developments in ARCH modelling which can be implemented using econometric software, model construction, fitting and forecasting and model evaluation and selection. Key Features: Presents a comprehensive overview of both the theory and the practical applications of ARCH, an increasingly popular financial modelling technique. Assumes no prior knowledge of ARCH models; the basics such as model construction are introduced, before proceeding to more complex applications such as value-at-risk, option pricing and model evaluation. Uses empirical examples to demonstrate how the recent developments inTrade Review"Numerous articles on the Autoregressive Conditional Heteroskedastic (ARCH) process, an increasingly popular financial modeling technique, exist in various international journals. Now Xekalaki and Degiannakis (both statistics, Athens U. of Economics and Business, Greece) provide a thorough treatment of the ARCH theory and its practical applications, in a textbook for postgraduate and final-year undergraduate students which could serve as reference work for academics and financial market professionals." (Book News Inc, November 2010) Table of ContentsPrologue. Notation. 1 What is an ARCH process? 1.1 Introduction. 1.2 The Autoregressive Conditionally Heteroskedastic Process. 1.3 The Leverage Effect. 1.4 The Non-trading Period Effect. 1.5 Non-synchronous Trading Effect. 1.6 The Relationship between Conditional Variance and Conditional Mean. 2 ARCH Volatility Specifications. 2.1 Model Specifications. 2.2 Methods of Estimation. 2.3. Estimating the GARCH Model with EViews 6: An Empirical Example.. 2.4. Asymmetric Conditional Volatility Specifications. 2.5. Simulating ARCH Models Using EViews. 2.6. Estimating Asymmetric ARCH Models with G@RCH 4.2 OxMetrics – An Empirical Example.. 2.7. Misspecification Tests. 2.8 Other ARCH Volatility Specifications. 2.9 Other Methods of Volatility Modeling. 2.10 Interpretation of the ARCH Process. 3 Fractionally Integrated ARCH Models. 3.1 Fractionally Integrated ARCH Model Specifications. 3.2 Estimating Fractionally Integrated ARCH Models Using G@RCH 4.2 OxMetrics – An Empirical Example. 3.3 A More Detailed Investigation of the Normality of the Standardized Residuals – Goodness-of-fit Tests. 4 Volatility Forecasting: An Empirical Example Using EViews 6. 4.1 One-step-ahead Volatility Forecasting. 4.2 Ten-step-ahead Volatility Forecasting. 5 Other Distributional Assumptions. 5.1 Non-Normally Distributed Standardized Innovations. 5.2 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using G@RCH 4.2 OxMetrics – An Empirical Example. 5.3 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – An Empirical Example. 5.4 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – The LogL Object. 6 Volatility Forecasting: An Empirical Example Using G@RCH Ox. 7 Intra-Day Realized Volatility Models. 7.1 Realized Volatility. 7.2 Intra-Day Volatility Models. 7.3 Intra-Day Realized Volatility & ARFIMAX Models in G@RCH 4.2 OxMetrics – An Empirical example. 8 Applications in Value-at-Risk, Expected Shortfalls, Options Pricing. 8.1 One-day-ahead Value-at-Risk Forecasting. 8.2 One-day-ahead Expected Shortfalls Forecasting. 8.3 FTSE100 Index: One-step-ahead Value-at-Risk and Expected Shortfall Forecasting. 8.4 Multi-period Value-at-Risk and Expected Shortfalls Forecasting. 8.5 ARCH Volatility Forecasts in Black and Scholes Option Pricing. 8.6 ARCH Option Pricing Formulas. 9 Implied Volatility Indices and ARCH Models. 9.1 Implied Volatility. 9.2 The VIX Index. 9.3 The Implied Volatility Index as an Explanatory Variable. 9.4 ARFIMAX Modeling for Implied Volatility Index. 10 ARCH Model Evaluation and Selection. 10.1 Evaluation of ARCH Models. 10.2 Selection of ARCH Models. 10.3 Application of Loss Functions as Methods of Model Selection.. 10.4 The SPA Test for VaR and Expected Shortfalls. 11 Multivariate ARCH Models. 11.1 Model Specifications. 11.2 Maximum Likelihood Estimation. 11.3 Estimating Multivariate ARCH Models Using EViews 6. 11.4 Estimating Multivariate ARCH Models Using G@RCH 5.0. 11.5 Evaluation of Multivariate ARCH Models. References. Author Index. Subject Index.

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Book SynopsisThe text has been thoroughly updated to incorporate recent developments and includes three major new chapters on: time series modelling in the financial economics area, the Harvey approach to structural time series modelling and cointegration, and panel data models and non--stationary time series.Table of ContentsPreface. 1. Introduction and Overview. Some Initial Concepts. Forecasting. Outline of the Book. 2. Short- and Long-run Models. Long-run Models. Stationary and Non-stationary Time Series. Spurious Regressions. Cointegration. Short-run Models. Conclusion. 3. Testing for Unit Roots. The Dickey–Fuller Test. Augmented Dickey–Fuller Test. Power and Level of Unit Root Tests. Structural Breaks and Unit Root Tests. Seasonal Unit Roots. Structural Breaks and Seasonal Unit Root Tests. Periodic Integration and Unit Root-testing. Conclusion on Unit Root Tests. 4. Cointegration in Single Equations. The Engle–Granger (EG) Approach. Testing for Cointegration with a Structural Break. Alternative Approaches. Problems with the Single Equation Approach. Estimating the Short-run Dynamic Model. Seasonal Cointegration. Periodic Cointegration. Asymmetric Tests for Cointegration. Conclusion s. 5. Cointegration in Multivariate Systems. The Johansen Approach. Testing the Order of Integration of the Variables. Formulation of the Dynamic Model. Testing for Reduced Rank. Deterministic Components in the Multivariate Model. Testing of Weak Exogeneity and VECM with Exogenous I (l) Variables. Testing for Linear Hypotheses on Cointegration Relations. Testing for Unique Cointegration Vectors. Joint Tests of Restrictions on α and β Seasonal Unit Roots. Seasonal Cointegration. Conclusions. Appendix 1: Programming in SHAZAM. 6. Modelling the Short-run Multivariate System. Introduction. Estimating the Long-run Cointegration Relationships. Parsimonious VECM. Conditional PVECM. Structural Modelling. Structural Macroeconomic Modelling. 7. Panel Data Models and Cointegration. Introduction. Panel Data and Modelling Techniques. Panel Unit Root Tests. Testing for Cointegration in Panels. Estimating Panel Cointegration Models. Conclusion on Testing for Unit Roots and Cointegration in Panel Data. 8. Modelling and Forecasting Financial Times Series. Introduction. ARCH and GARCH. Multivariate GARCH. Estimation and Testing. An Empirical Application of ARCH and GARCH Models. ARCH-M. Asymmetric GARCH Models. Integrated and Fractionally Integrated GARCH Models. Conditional Heteroscedasticity, Unit Roots and Cointegration. Forecasting with GARCH Models. Further Methods for Forecast Evaluation. Conclusions on Modelling and Forecasting Financial Time Series. Appendix: Cointegration Analysis Using the Johansen Technique: A Practitioner’s Guide to PcGive 10.1. Statistical Appendix. References. Index.

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Book SynopsisA complete set of statistical tools for beginning financial analysts from a leading authority Written by one of the leading experts on the topic, An Introduction to Analysis of Financial Data with R explores basic concepts of visualization of financial data. Through a fundamental balance between theory and applications, the book supplies readers with an accessible approach to financial econometric models and their applications to real-world empirical research. The author supplies a hands-on introduction to the analysis of financial data using the freely available R software package and case studies to illustrate actual implementations of the discussed methods. The book begins with the basics of financial data, discussing their summary statistics and related visualization methods. Subsequent chapters explore basic time series analysis and simple econometric models for business, finance, and economics as well as related topics including: LinearTrade Review“I found this book highly informative and interesting to read. The proper mix of theory and hands-on programming examples makes it recommended reading for both R programmers interested in finance and financial analysts with a basic programming background. Well written and following a clear and defined logical layout, the author has written a current reference text on using a powerful open-source programming language for typical financial analysis.” (Computing Reviews, 25 March 2014) “All in all, this book is a good and useful introduction to financial time series with many real-world examples. It is suitable for use both as a textbook and for self-study, with exercises provided at the end of each chapter.” (International Statistical Review, 14 June 2013) Table of ContentsPreface xiii 1 FINANCIAL DATA AND THEIR PROPERTIES 1 1.1 Asset Returns 2 1.2 Bond Yields and Prices 7 1.3 Implied Volatility 10 1.4 R Packages and Demonstrations 12 1.4.1 Installation of R Packages 12 1.4.2 The Quantmod Package 12 1.4.3 Some Basic R Commands 16 1.5 Examples of Financial Data 17 1.6 Distributional Properties of Returns 20 1.6.1 Review of Statistical Distributions and Their Moments 20 1.7 Visualization of Financial Data 27 1.8 Some Statistical Distributions 32 1.8.1 Normal Distribution 32 1.8.2 Lognormal Distribution 32 1.8.3 Stable Distribution 33 1.8.4 Scale Mixture of Normal Distributions 33 1.8.5 Multivariate Returns 34 Exercises 36 References 37 2 LINEAR MODELS FOR FINANCIAL TIME SERIES 39 2.1 Stationarity 40 2.2 Correlation and Autocorrelation Function 43 2.3 White Noise and Linear Time Series 50 2.4 Simple Autoregressive Models 51 2.4.1 Properties of AR Models 52 2.4.2 Identifying AR Models in Practice 60 2.4.3 Goodness of Fit 67 2.4.4 Forecasting 67 2.5 Simple Moving Average Models 69 2.5.1 Properties of MA Models 72 2.5.2 Identifying MA Order 73 2.5.3 Estimation 74 2.5.4 Forecasting Using MA Models 75 2.6 Simple ARMA Models 78 2.6.1 Properties of ARMA(1,1) Models 79 2.6.2 General ARMA Models 80 2.6.3 Identifying ARMA Models 81 2.6.4 Forecasting Using an ARMA Model 84 2.6.5 Three Model Representations for an ARMA Model 84 2.7 Unit-Root Nonstationarity 86 2.7.1 Random Walk 86 2.7.2 Random Walk with Drift 88 2.7.3 Trend-Stationary Time Series 90 2.7.4 General Unit-Root Nonstationary Models 91 2.7.5 Unit-Root Test 91 2.8 Exponential Smoothing 96 2.9 Seasonal Models 98 2.9.1 Seasonal Differencing 99 2.9.2 Multiplicative Seasonal Models 101 2.9.3 Seasonal Dummy Variable 107 2.10 Regression Models with Time Series Errors 110 2.11 Long-Memory Models 117 2.12 Model Comparison and Averaging 120 2.12.1 In-sample Comparison 120 2.12.2 Out-of-sample Comparison 121 2.12.3 Model Averaging 125 Exercises 125 References 127 3 CASE STUDIES OF LINEAR TIME SERIES 128 3.1 Weekly Regular Gasoline Price 129 3.1.1 Pure Time Series Model 130 3.1.2 Use of Crude Oil Prices 133 3.1.3 Use of Lagged Crude Oil Prices 134 3.1.4 Out-of-Sample Predictions 135 3.2 Global Temperature Anomalies 140 3.2.1 Unit-Root Stationarity 141 3.2.2 Trend-Nonstationarity 145 3.2.3 Model Comparison 148 3.2.4 Long-Term Prediction 150 3.2.5 Discussion 153 3.3 US Monthly Unemployment Rates 157 3.3.1 Univariate Time Series Models 157 3.3.2 An Alternative Model 161 3.3.3 Model Comparison 165 3.3.4 Use of Initial Jobless Claims 165 3.3.5 Comparison 173 Exercises 174 References 175 4 ASSET VOLATILITY AND VOLATILITY MODELS 176 4.1 Characteristics of Volatility 177 4.2 Structure of a Model 178 4.3 Model Building 181 4.4 Testing for ARCH Effect 182 4.5 The ARCH Model 185 4.5.1 Properties of ARCH Models 186 4.5.2 Advantages and Weaknesses of ARCH Models 187 4.5.3 Building an ARCH Model 188 4.5.4 Some Examples 193 4.6 The GARCH Model 199 4.6.1 An Illustrative Example 201 4.6.2 Forecasting Evaluation 210 4.6.3 A Two-Pass Estimation Method 210 4.7 The Integrated GARCH Model 211 4.8 The GARCH-M Model 213 4.9 The Exponential Garch Model 215 4.9.1 An Illustrative Example 217 4.9.2 An Alternative Model Form 218 4.9.3 Second Example 218 4.9.4 Forecasting Using an EGARCH Model 220 4.10 The Threshold Garch Model 222 4.11 Asymmetric Power ARCH Models 224 4.12 Nonsymmetric GARCH Model 226 4.13 The Stochastic Volatility Model 228 4.14 Long-Memory Stochastic Volatility Models 230 4.15 Alternative Approaches 232 4.15.1 Use of High Frequency Data 232 4.15.2 Use of Daily Open, High, Low, and Close Prices 235 Exercises 239 References 241 5 APPLICATIONS OF VOLATILITY MODELS 243 5.1 Garch Volatility Term Structure 244 5.1.1 Term Structure 246 5.2 Option Pricing and Hedging 248 5.3 Time-Varying Correlations and Betas 251 5.3.1 Time-Varying Betas 256 5.4 Minimum Variance Portfolios 259 5.5 Prediction 263 Exercises 271 References 272 6 HIGH FREQUENCY FINANCIAL DATA 274 6.1 Nonsynchronous Trading 275 6.2 Bid–Ask Spread of Trading Prices 279 6.3 Empirical Characteristics of Trading Data 282 6.4 Models for Price Changes 285 6.4.1 Ordered Probit Model 288 6.4.2 A Decomposition Model 293 6.5 Duration Models 298 6.5.1 Diurnal Component 299 6.5.2 The ACD Model 301 6.5.3 Estimation 303 6.6 Realized Volatility 308 6.6.1 Handling Microstructure Noises 313 6.6.2 Discussion 317 Appendix A: Some Probability Distributions 320 Appendix B: Hazard Function 323 Exercises 324 References 325 7 VALUE AT RISK 327 7.1 Risk Measure and Coherence 328 7.1.1 Value at Risk (VaR) 329 7.1.2 Expected Shortfall 334 7.2 Remarks on Calculating Risk Measures 336 7.3 Riskmetrics 337 7.3.1 Discussion 342 7.3.2 Multiple Positions 343 7.4 An Econometric Approach 345 7.4.1 Multiple Periods 348 7.5 Quantile Estimation 352 7.5.1 Quantile and Order Statistics 353 7.5.2 Quantile Regression 354 7.6 Extreme Value Theory 358 7.6.1 Review of Extreme Value Theory 358 7.6.2 Empirical Estimation 361 7.6.3 Application to Stock Returns 363 7.7 An Extreme Value Approach to Var 368 7.7.1 Discussion 370 7.7.2 Multiperiod VaR 371 7.7.3 Return Level 371 7.8 Peaks Over Thresholds 372 7.8.1 Statistical Theory 373 7.8.2 Mean Excess Function 374 7.8.3 Estimation 376 7.8.4 An Alternative Parameterization 378 7.9 The Stationary Loss Processes 381 Exercises 383 References 384 Index 387

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Book SynopsisThe Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T.W.Table of ContentsThe Use of Regression Analysis. Trends and Smoothing. Cyclical Trends. Linear Stochastic Models with Finite Numbers of Parameters. Serial Correlation. Stationary Stochastic Processes. The Sample Mean, Covariances, and Spectral Density. Estimation of the Spectral Density. Linear Trends with Stationary Random Terms. Appendices. Bibliography. Index.

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Book SynopsisIn this text on statistical decision-making, the authors use examples such as computing values for the stock market, conducting market research reports or using an options pricing model to illuminate the subject matter.Table of ContentsIntroduction to Quantitative Decision Making. Discrete Probability and Decision Analysis. Decision Making with Binomial and Normal Probabilities. Decisions Based on Sample Statistics. Sample Design and Estimation. Decisions Based on Linear Relationships. Hypothesis Testing. Quality Control. Forecasting. Analysis of Variance. Simulation. Linear Programming. Appendices. Data Disk Files. Selected References. Answers to Even-Numbered Problems. Index.

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Book SynopsisA comprehensive guide to financial econometrics Financial econometrics is a quest for models that describe financial time series such as prices, returns, interest rates, and exchange rates. In Financial Econometrics, readers will be introduced to this growing discipline and the concepts and theories associated with it, including background material on probability theory and statistics. The experienced author team uses real-world data where possible and brings in the results of published research provided by investment banking firms and journals. Financial Econometrics clearly explains the techniques presented and provides illustrative examples for the topics discussed. Svetlozar T. Rachev, PhD (Karlsruhe, Germany) is currently Chair-Professor at the University of Karlsruhe. Stefan Mittnik, PhD (Munich, Germany) is Professor of Financial Econometrics at the University of Munich. Frank J. Fabozzi, PhD, CFA, CFP (New Hope, PA) is an adjunct professor of Finance at Yale UniversiTable of ContentsPreface. Abbreviations and Acronyms. About the Authors. CHAPTER 1: Financial Econometrics: Scope and Methods. The Data Generating Process. Financial Econometrics at Work. Time Horizon of Models. Applications. Appendix: Investment Management Process. Concepts Explained in this Chapter (in order of presentation). CHAPTER 2: Review of Probability and Statistics. Concepts of Probability. Principles of Estimation. Bayesian Modeling. Appendix A: Information Structures. Appendix B: Filtration. Concepts Explained in this Chapter (in order of presentation). CHAPTER 3: Regression Analysis: Theory and Estimation. The Concept of Dependence. Regressions and Linear Models. Estimation of Linear Regressions. Sampling Distributions of Regressions. Determining the Explanatory Power of a Regression. Using Regression Analysis in Finance. Stepwise Regression. Nonnormality and Autocorrelation of the Residuals. Pitfalls of Regressions. Concepts Explained in this Chapter (in order of presentation) . CHAPTER 4: Selected Topics in Regression Analysis. Categorical and Dummy Variables in Regression Models. Constrained Least Squares. The Method of Moments and its Generalizations. Concepts Explained in this Chapter (in order of presentation). CHAPTER 5: Regression Applications in Finance. Applications to the Investment Management Process. A Test of Strong-Form Pricing Efficiency. Tests of the CAPM. Using the CAPM to Evaluate Manager Performance: The Jensen Measure. Evidence for Multifactor Models. Benchmark Selection: Sharpe Benchmarks. Return-Based Style Analysis for Hedge Funds. Hedge Fund Survival. Bond Portfolio Applications. Concepts Explained in this Chapter (in order of presentation). CHAPTER 6: Modeling Univariate Time Series. Difference Equations. Terminology and Definitions. Stationarity and Invertibility of ARMA Processes. Linear Processes. Identification Tools. Concepts Explained in this Chapter (in order of presentation). CHAPTER 7: Approaches to ARIMA Modeling and Forecasting. Overview of Box-Jenkins Procedure. Identification of Degree of Differencing. Identification of Lag Orders. Model Estimation. Diagnostic Checking. Forecasting. Concepts Explained in this Chapter (in order of presentation). CHAPTER 8: Autoregressive Conditional Heteroskedastic Models. ARCH Process. GARCH Process. Estimation of the GARCH Models. Stationary ARMA-GARCH Models. Lagrange Multiplier Test. Variants of the GARCH Model. GARCH Model with Student’s t-Distributed Innovations. Multivariate GARCH Formulations. Appendix: Analysis of the Properties of the GARCH(1,1) Model. Concepts Explained in this Chapter (in order of presentation). CHAPTER 9: Vector Autoregressive Models I. VAR Models Defined. Stationary Autoregressive Distributed Lag Models. Vector Autoregressive Moving Average Models. Forecasting with VAR Models. Appendix: Eigenvectors and Eigenvalues. Concepts Explained in this Chapter (in order of presentation). CHAPTER 10: Vector Autoregressive Models II. Estimation of Stable VAR Models. Estimating the Number of Lags. Autocorrelation and Distributional Properties of Residuals. VAR Illustration. Concepts Explained in this Chapter (in order of presentation). CHAPTER 11: Cointegration and State Space Models. Cointegration. Error Correction Models. Theory and Methods of Estimation of Nonstationary VAR Models. State-Space Models. Concepts Explained in this Chapter (in order of presentation). CHAPTER 12: Robust Estimation. Robust Statistics. Robust Estimators of Regressions. Illustration: Robustness of the Corporate Bond Yield Spread Model. Concepts Explained in this Chapter (in order of presentation). CHAPTER 13: Principal Components Analysis and Factor Analysis. Factor Models. Principal Components Analysis. Factor Analysis. PCA and Factor Analysis Compared. Concepts Explained in this Chapter (in order of presentation). CHAPTER 14: Heavy-Tailed and Stable Distributions in Financial Econometrics. Basic Facts and Definitions of Stable Distributions. Properties of Stable Distributions. Estimation of the Parameters of the Stable Distribution. Applications to German Stock Data. Appendix: Comparing Probability Distributions. Concepts Explained in this Chapter (in order of presentation). CHAPTER 15: ARMA and ARCH Models with Infinite-Variance Innovations. Infinite Variance Autoregressive Processes. Stable GARCH Models. Estimation for the Stable GARCH Model. Prediction of Conditional Densities. Concepts Explained in this Chapter (in order of presentation). APPENDIX: Monthly Returns for 20 Stocks: December 2000–November 2005. INDEX.

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Book SynopsisGlobal and combinatorial optimization heuristics are widely used in different areas ranging from engineering to operational research. This introduction to the fast growing field of optimization heuristics offers the knowledge to use the techniques in a number of different application areas.Trade Review"For statisticians and econometricians with a general interest in new optimization paradigms, Winker...introduces optimization heuristics for application..." (Reference Research Book News, Vol. 16, No. 3, August 2001) "...a very fine textbook ... does an excellent job of motivating ones . interests in optimization heuristics." (Technometrics, Vol. 43, No. 4, November 2001) "a text that comprehensively addresses this 'art' is to be congratulated..." (Short Book Reviews, August 2002) ..."The book is recommend ... the postgraduate students the book provides a valuable introduction to optimization heuristics." (Zentralblatt MATH, Vol.1001, No.01, 2003)Table of ContentsPreface. Introduction. OPTIMIZATION IN STATISTICS AND ECONOMETRICS. Optimization in Economics. Optimization in Statistics and Econometrics. The Heuristic Optimization Paradigm. HEURISTIC OPTIMIZATION: THRESHOLD ACCEPTING. Optimization Methods. The Global Optimization Heuristic Threshold Accepting. Relative Performance of Threshold Accepting. Tuning of Threshold Accepting. A Practical Guide to the Implementation of Threshold Accepting. APPLICATIONS IN STATISTICS AND ECONOMETRICS. Introduction. Experimental Design. Identification of Multivariate Lag Structures. Optimal Aggregation. Censored Quantile Regression. Continuous Global Optimization. CONCLUSION AND OUTLOOK. Conclusion. Outlook for Further Research. References. List of Symbols. Author Index. Subject Index.

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Book SynopsisThe authors reconsider the problem of parametrically specifying distribution suitable for asset--return models. They describe alternative distributions, showing how they can be estimated and applied to stock--index and exchange--rate data. The implications for options pricing are also investigated.Table of ContentsForeword Preface 1 Introduction 2 Univariate Stable Distributions 3 Identification, Estimation and Goodness of Fit 4 Empirical Comparison 5 Subordinated, Fractional Stable and Stable ARIMA Processes 6 ARCH-type and Shot Noise Processes 7 Multivariate Stable Models 8 Estimation, Association, Risk, and Symmetry of Stable Portfolios 9 Asset-Pricing and Portfolio Theory Under Stable Paretian Laws 10 Risk Management: Value at Risk for Heavy-Tailed Distributed Rating 11 Option Pricing Under Alternative Stable Models 12 Option Pricing for Infinitely Divisible Return Models 13 Numerical Results on Option Pricing: Modeling and Forecasting 14 Stable Models in Econometrics 15 Stable Paretian Econometrics: Unit-Root Theory and Cointegrated Models References Indexes Author-Index Subject-Index

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Book SynopsisThis work aims to serve two primary purposes: first, to present findings regarding the age and related characteristics of corporations within the private enterprise system. The research seeks to provide insights into corporate behavior and potential implications for both private and public policy, acknowledging that some conclusions may be open to debate and may inspire differing interpretations from future researchers. To support such re-evaluation, the book offers a detailed explanation of the analytical methods employed, hoping to aid further investigation and refinement by others in the field. The second purpose is to stimulate greater interest in the study of corporate vital statistics, illustrating how various significant inferences can be drawn from a specific set of data. The author hopes this work will encourage the collection of more comprehensive and detailed corporate statistics, which could remove certain analytical limitations encountered here. This study is positioned as an initial exploration, not a final statement; with better data and refined methods from subsequent research, the findings may soon be surpassed, thereby achieving the goal of inspiring more advanced inquiries. The author acknowledges valuable support from collaborators who contributed significantly to data handling and preparation, including Mrs. Harriet Ross and the Bureau of Business and Economic Research at the University of California, Berkeley. Their assistance lightened the burden of this extensive project; however, any errors or misinterpretations are the author's responsibility alone. This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1953. ,

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Book SynopsisThis text prepares first-year graduate students and advanced undergraduates for empirical research in economics, and also equips them for specialization in econometric theory, business, and sociology.Trade ReviewThis book is an excellent choice for first year graduate econometrics courses because it provides a solid foundation in statistical reasoning in a manner that is both clear and concise. It addresses a number of issues that are of central importance to developing practitioners and theorists alike and achieves this in a fairly nontechnical manner… The topics addressed here are rarely given such a thorough treatment in econometrics textbooks. For example, in discussions of bivariate distributions, Goldberger points out that two uncorrelated normal random variables may not be independent, since a nonnormal bivariate distribution can generate normal marginal distributions. Other texts typically leave readers with the impression that two uncorrelated normal random variables are independent without reference to their joint distribution… A Course in Econometrics is rigorous, it makes students think hard about important issues, and it avoids a cookbook approach. For these reasons, I strongly recommend it as a basic text for all first year graduate econometrics courses. -- Douglas G. Steigerwald * Econometric Theory *[A Course in Econometrics] strike[s] the right balance between mathematical rigour and intuitive feel. It aims to prepare students for empirical research but also those who go on to more advanced econometrics… The book is very clear and very precise. It is built on just a few very simple concepts. I think that students will like it very much. I congratulate Professor Goldberger with having written a very useful book. -- Jan R. Magnus * Economic Journal *Undoubtedly the best Ph.D. level econometrics textbook available today. The analogy principle of estimation serves to unify the treatment of a wide range of topics that are at the foundation of empirical economics. The notation is concise and consistently used throughout the text… Students have expressed delight in unraveling the proofs and lemmas. It’s a pleasure to teach from this book. Recommended for any serious economics student or anyone interested in studying the principles underlying applied economics. -- Michael Hazilla, American UniversityTable of Contents1. Empirical Relations 1.1 Theoretical and Empirical Relations 1.2 Sample Means and Population Means 1.3 Sampling 1.4 Estimation Exercises 2. Univariate Probability Distributions 2.1 Introduction 2.2 Discrete Case 2.3 Continuous Case 2.4 Mixed Case 2.5 Functions of Random Variables Exercises 3. Expectations: Univariate Case 3.1 Expectations 3.2 Moments 3.3 Theorems on Expectations 3.4 Prediction 3.5 Expectations and Probabilities Exercises 4. Bivariate Probability Distributions 4.1 Joint Distributions 4.2 Marginal Distributions 4.3 Conditional Distributions Exercises 5. Expectations Bivariate Case 5.1 Expectations 5.2 Conditional Expectations 5.3 Conditional Expectation Function 5.4 Prediction 5.5 Conditional Expectations and Linear Predictors Exercises 6. lndependence in a Bivariate Distribution 6.1 Introduction 6.2 Stochastic Independence 6.3 Roles of Stochastic Independence 6.4 Mean-Independence and Uncorrelatedness 6.5 Types of Independence 6.6 Strength of a Relation Exercises 7. Normal Distributions 7.1 Univariate Normal Distribution 7.2 Standard Bivariate Normal Distribution 7.3 Bivariate Normal Distribution 7.4 Properties of Bivariate Normal Distribution 7.5 Remarks Exercises 8. Sampling Distributions Univariate Case 8.1 Random Sample 8.2 Sample Statistics 8.3 The Sample Mean 8.4 Sample Moments 8.5 Chi-square and Student's Distributions 8.6 Sampling from a Normal Population Exercises 9. Asymptotic Distribution Theory 9.1 Introduction 9.2 Sequences of Sample Statistics 9.3 Asymptotics of the Sample Mean 9.4 Asymptotics of Sample Moments 9.5 Asymptotics of Functions of Sample Moments 9.6 Asymptotics of Some Sample Statistics Exercises 10. Sampling Distributions Bivariate Case 10.1 Introduction 10.2 Sample Covariance 10.3 Pair of Sample Means 10.4 Ratio of Sample Means 10.5 Sample Slope 10.6 Variance of Sample Slope Exercises 11. Parameter Estimation 11.1 Introduction 11.2 The Analogy Principle 11.3 Criteria for an Estimator 11.4 Asymptotic Criteria 11.5 Confidence Intervals Exercises 12. Advanced Estimation Theory 12.1 The Score Variable 12.2 Cramer-Rao Inequality 12.3 ZES-Rule Estimation 12.4 Maximum Likelihood Estimation Exercises 13. Estimating a Population Relation 13.1 Introduction 13.2 Estimating a Linear CEF 13.3 Estimating a Nonlinear CEF 13.4 Estimating a Binary Response Model 13.5 Other Sampling Schemes Exercises 14. Multiple Regression 14.1 Population Regression Function 14.2 Algebra for Multiple Regression 14.3 Ranks of X and Q 14.4 The Short-Rank Case 14.5 Second-Order Conditions Exercises 15. Classical Regression 15.1 Matrix Algebra for Random Variables 15.2 Classical Regression Model 15.3 Estimation of beta165 15.4 Gauss-Markov Theorem 15.5 Estimation of delta2 and V(b) Exercises 16. Classical Regression Interpretation and Application 16.1 Interpretation of the Classical Regression Model 16.2 Estimation of Linear Functions of beta13 16.3 Estimation of Conditional Expectation, and Prediction 16.4 Measuring Goodness of Fit Exercises 17. Regression Algebra 17.1 Regression Matrices 17.2 Short and Long Regression Algebra 17.3 Residual Regression 17.4 Applications of Residual Regression 17.5 Short and Residual Regressions in the Classical Regression Model Exercises 18. Multivariate Normal Distribution 18.1 Introduction 18.2 Multivariate Normality 18.3 Functions of a Standard Normal Vector 18.4 Quadratic Forms in Normal Vectors Exercises 19. Classical Normal Regression 19.1 Classical Normal Regression Model 19.2 Maximum Likelihood Estimation 19.3 Sampling Distributions 19.4 Confidence Intervals 19.5 Confidence Regions 19.6 Shape of the Joint Confidence Region Exercises 20. CNR Model Hypothesis Testing 20.1 Introduction 20.2 Test on a Single Parameter 20.3 Test on a Set of Parameters 20.4 Power of the Test 20.5 Noncentral Chi-square Distribution Exercises 21. CNR Model Inference with Unknown 21.1 Distribution Theory 21.2 Confidence Intervals and Regions 21.3 Hypothesis Tests 21.4 Zero Null Subvector Hypothesis Exercises 22. Issues in Hypothesis Testing 22.1 Introduction 22.2 General Linear Hypothesis 22.3 One-Sided Alternatives 22.4 Choice of Significance Level 22.5 Statistical versus Economic Significance 22.6 Using Asymptotics 22.7 Inference without Normality Assumption Exercises 23. Multicollinearity 23.1 Introduction 23.2 Textbook Discussions 23.3 Micronumerosity 23.4 When Multicollinearity Is Desirable 23.5 Remarks Exercises 24. Regression Strategies 24.1 Introduction 24.2 Shortening a Regression 24.3 Mean Squared Error 24.4 Pretest Estimation 24.5 Regression Fishing Exercises 25. Regression with X Random 25.1 Introduction 25.2 Neoclassical Regression Model 25.3 Properties of Least Squares Estimation 25.4 Neoclassical Normal Regression Model 25.5 Asymptotic Properties of Least Squares Estimation Exercises 26. Time Series 26.1 Departures from Random Sampling 26.2 Stationary Population Model 26.3 Conditional Expectation Functions 26.4 Stationary Processes 26.5 Sampling and Estimation 26.6 Remarks Exercises 27. Generalized Classical Regression 27.1 Generalized Classical Regression Model 27.2 Least Square Estimation 27.3 Generalized Least Square Estimation 27.4 Remarks on GL Estimation 27.5 Feasible Generalized Least Squares Estimation 27.6 Extensions of the GCR Model Exercises 28. Heteroskedasticity and Autocorrelation 28.1 Introduction 28.2 Pure Heteroskedasticity 28.3 First-Order Autoregressive Process 28.4 Remarks Exercises 29. Nonlinear Regression 29.1 Nonlinear CEF's 29.2 Estimation 29.3 Computation of the Nonlinear Least Squares Estimator 29.4 Asymptotic Properties 29.5 Probit Model Exercises 30. Regression Systems 30.1 Introduction 30.2 Stacking 30.3 Generalized Least Squares 30.4 Comparison of GLS and LS Estimators 30.5 Feasible Generalized Least Squares 30.6 Restrictions 30.7 Alternative Estimators Exercises 31. Structural Equation Models 31.1 Introduction 31.2 Permanent Income Model 31.3 Keynesian Model 31.4 Estimation of the Keynesian Model 31.5 Structure versus Regression Exercises 32. Simultaneous-Equation Model 32.1 A Supply-Demand Model 32.2 Specification of the Simultaneous-Equation Model 32.3 Sampling 32.4 Remarks 33. Identification and Restrictions 33.1 Introduction 33.2 Supply-Demand Models 33.3 Uncorrelated Disturbances 33.4 Other Sources of Identification Exercises 34. Estimation in the Simultaneous-Equation Model 34.1 Introduction 34.2 Indirect Feasible Generalized Least Squares 34.3 Two-Stage Least Squares 34.4 Relation between 2SLS and Indirect-FGLS

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Book SynopsisDemonstrates the analytical benefits acquired when an analysis with a representative consumer is possible, they also characterize the restrictiveness of assumptions under which a representative household justifies a purely aggregative analysis.Trade ReviewLars Peter Hansen, Co-Winner of the 2013 Nobel Prize in Economics Thomas J. Sargent, Winner of the 2011 Nobel Prize in EconomicsTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xiii*Acknowledgments, pg. xv*Chapter 1. Theory and Econometrics, pg. 3*Chapter 2. Linear Stochastic Difference Equations, pg. 15*Chapter 3. Efficient Computations, pg. 33*Chapter 4. Economic Environments, pg. 61*Chapter 5. Optimal Resource Allocations, pg. 79*Chapter 6. A Commodity Space, pg. 125*Chapter 7. Competitive Economies, pg. 131*Chapter 8. Statistical Representations, pg. 153*Chapter 9. Canonical Household Technologies, pg. 191*Chapter 10. Examples, pg. 217*Chapter 11. Permanent IncomeModels, pg. 233*Chapter 12. Gorman Heterogeneous Households, pg. 253*Chapter 13. Complete Markets Aggregation, pg. 269*Chapter 14. Periodic Models of Seasonality, pg. 291*Appendix A. MATLAB Programs, pg. 327*References, pg. 379*Subject Index, pg. 393*Author Index, pg. 397*MATLAB Index, pg. 399*The Gorman Lectures in Economics, pg. 401

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Book SynopsisThe key issue confronting empirical economics is to establish sustainable relationships that are both supported by data and interpretable from economic theory. Focusing on modeling, this book aims to give students the statistical foundations of estimation and inference, and also presents a thorough understanding of econometric techniques.Trade Review"Hendry and Nielsen's somewhat unusual data-driven approach works well...providing genuine insights at a reasonably advanced level."--John Hudson, Times Higher Education "Summing up: A remarkable achievement, a beautiful piece of work, engaging the reader quickly with the subject matter, Econometric Modeling provides a good introduction to the field for aspiring and advanced students and also contains valuable material and hints for experts already well versed in the subject. A must-buy for the library."--Current Engineering PracticeTable of ContentsPreface ix Data and software xi Chapter 1: The Bernoulli model 1 1.1 Sample and population distributions 1 1.2 Distribution functions and densities 4 1.3 The Bernoulli model 6 1.4 Summary and exercises 12 Chapter 2: Inference in the Bernoulli model 14 2.1 Expectation and variance 14 2.2 Asymptotic theory 19 2.3 Inference 23 2.4 Summary and exercises 26 Chapter 3: A first regression model 28 3.1 The US census data 28 3.2 Continuous distributions 29 3.3 Regression model with an intercept 32 3.4 Inference 38 3.5 Summary and exercises 42 Chapter 4: The logit model 47 4.1 Conditional distributions 47 4.2 The logit model 52 4.3 Inference 58 4.4 Mis-specification analysis 61 4.5 Summary and exercises 63 Chapter 5: The two-variable regression model 66 5.1 Econometric model 66 5.2 Estimation 69 5.3 Structural interpretation 76 5.4 Correlations 78 5.5 Inference 81 5.6 Summary and exercises 85 Chapter 6: The matrix algebra of two-variable regression 88 6.1 Introductory example 88 6.2 Matrix algebra 90 6.3 Matrix algebra in regression analysis 94 6.4 Summary and exercises 96 Chapter 7: The multiple regression model 98 7.1 The three-variable regression model 98 7.2 Estimation 99 7.3 Partial correlations 104 7.4 Multiple correlations 107 7.5 Properties of estimators 109 7.6 Inference 110 7.7 Summary and exercises 118 Chapter 8: The matrix algebra of multiple regression 121 8.1 More on inversion of matrices 121 8.2 Matrix algebra of multiple regression analysis 122 8.3 Numerical computation of regression estimators 124 8.4 Summary and exercises 126 Chapter 9: Mis-specification analysis in cross sections 127 9.1 The cross-sectional regression model 127 9.2 Test for normality 128 9.3 Test for identical distribution 131 9.4 Test for functional form 134 9.5 Simultaneous application of mis-specification tests 135 9.6 Techniques for improving regression models 136 9.7 Summary and exercises 138 Chapter 10: Strong exogeneity 140 10.1 Strong exogeneity 140 10.2 The bivariate normal distribution 142 10.3 The bivariate normal model 145 10.4 Inference with exogenous variables 150 10.5 Summary and exercises 151 Chapter 11: Empirical models and modeling 154 11.1 Aspects of econometric modeling 154 11.2 Empirical models 157 11.3 Interpreting regression models 161 11.4 Congruence 166 11.5 Encompassing 169 11.6 Summary and exercises 173 Chapter 12: Autoregressions and stationarity 175 12.1 Time-series data 175 12.2 Describing temporal dependence 176 12.3 The first-order autoregressive model 178 12.4 The autoregressive likelihood 179 12.5 Estimation 180 12.6 Interpretation of stationary autoregressions 181 12.7 Inference for stationary autoregressions 187 12.8 Summary and exercises 188 Chapter 13: Mis-specification analysis in time series 190 13.1 The first-order autoregressive model 190 13.2 Tests for both cross sections and time series 190 13.3 Test for independence 192 13.4 Recursive graphics 195 13.5 Example: finding a model for quantities of fish 197 13.6 Mis-specification encompassing 200 13.7 Summary and exercises 201 Chapter 14: The vector autoregressive model 203 14.1 The vector autoregressive model 203 14.2 A vector autoregressive model for the fish market 205 14.3 Autoregressive distributed-lag models 213 14.4 Static solutions and equilibrium-correction forms 214 14.5 Summary and exercises 215 Chapter 15: Identification of structural models 217 15.1 Under-identified structural equations 217 15.2 Exactly-identified structural equations 222 15.3 Over-identified structural equations 227 15.4 Identification from a conditional model 231 15.5 Instrumental variables estimation 234 15.6 Summary and exercises 237 Chapter 16: Non-stationary time series 240 16.1 Macroeconomic time-series data 240 16.2 First-order autoregressive model and its analysis 242 16.3 Empirical modeling of UK expenditure 243 16.4 Properties of unit-root processes 245 16.5 Inference about unit roots 248 16.6 Summary and exercises 252 Chapter 17: Cointegration 254 17.1 Stylized example of cointegration 254 17.2 Cointegration analysis of vector autoregressions 255 17.3 A bivariate model for money demand 258 17.4 Single-equation analysis of cointegration 267 17.5 Summary and exercises 268 Chapter 18: Monte Carlo simulation experiments 270 18.1 Monte Carlo simulation 270 18.2 Testing in cross-sectional regressions 273 18.3 Autoregressions 277 18.4 Testing for cointegration 281 18.5 Summary and exercises 285 Chapter 19: Automatic model selection 286 19.1 The model 286 19.2 Model formulation and mis-specification testing 287 19.3 Removing irrelevant variables 288 19.4 Keeping variables that matter 290 19.5 A general-to-specific algorithm 292 19.6 Selection bias 293 19.7 Illustration using UK money data 298 19.8 Summary and exercises 300 Chapter 20: Structural breaks 302 20.1 Congruence in time series 302 20.2 Structural breaks and co-breaking 304 20.3 Location shifts revisited 307 20.4 Rational expectations and the Lucas critique 308 20.5 Empirical tests of the Lucas critique 311 20.6 Rational expectations and Euler equations 315 20.7 Summary and exercises 319 Chapter 21: Forecasting 323 21.1 Background 323 21.2 Forecasting in changing environments 326 21.3 Forecasting from an autoregression 327 21.4 A forecast-error taxonomy 332 21.5 Illustration using UK money data 337 21.6 Summary and exercises 340 Chapter 22: The way ahead 342 References 345 Author index 357 Subject index 359

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Book SynopsisMoving beyond purely theoretical models, the author applies methods supported by empirical research of equity and foreign exchange markets to show how daily and more frequent asset prices, and the prices of option contracts, can be used to construct and assess predictions about future prices, their volatility, and their probability distributions.Trade ReviewWinner of the 2005 BestBook Award, Riskbook.com "This book provides thorough, well-presented and concise coverage of asset price dynamics and manages to combine new developments, established issues, theory and application in a practical and refreshing manner. It is well illustrated with time series graphs and tables and has a good balance between theoretical concepts and their practical applications with a mathematical treatment that is not too specialized."--Anthony F. Gyles, RSSTable of ContentsPreface xiii Chapter 1: Introduction 1 1.1 Asset Price Dynamics 1 1.2 Volatility 1 1.3 Prediction 2 1.4 Information 2 1.5 Contents 3 1.6 Software 5 1.7 Web Resources 6 PART I: Foundations 7 Chapter 2: Prices and Returns 9 2.1 Introduction 9 2.2 Two Examples of Price Series 9 2.3 Data-Collection Issues 10 2.4 Two Returns Series 13 2.5 Definitions of Returns 14 2.6 Further Examples of Time Series of Returns 19 Chapter 3: Stochastic Processes: Definitions and Examples 23 3.1 Introduction 23 3.2 Random Variables 24 3.3 Stationary Stochastic Processes 30 3.4 Uncorrelated Processes 33 3.5 ARMA Processes 36 3.6 Examples of ARMA 1 1 Specifications 44 3.7 ARIMA Processes 46 3.8 ARFIMA Processes 46 3.9 Linear Stochastic Processes 48 3.10 Continuous-Time Stochastic Processes 49 3.11 Notation for Random Variables and Observations 50 Chapter 4: Stylized Facts for Financial Returns 51 4.1 Introduction 51 4.2 Summary Statistics 52 4.3 Average Returns and Risk Premia 53 4.4 Standard Deviations 57 4.5 Calendar Effects 59 4.6 Skewness and Kurtosis 68 4.7 The Shape of the Returns Distribution 69 4.8 Probability Distributions for Returns 73 4.9 Autocorrelations of Returns 76 4.10 Autocorrelations of Transformed Returns 82 4.11 Nonlinearity of the Returns Process 92 4.12 Concluding Remarks 93 4.13 Appendix: Autocorrelation Caused by Day-of-the-Week Effects 94 4.14 Appendix: Autocorrelations of a Squared Linear Process 95 PART II: Conditional Expected Returns 97 Chapter 5: The Variance-Ratio Test of the Random Walk Hypothesis 99 5.1 Introduction 99 5.2 The Random Walk Hypothesis 100 5.3 Variance-Ratio Tests 102 5.4 An Example of Variance-Ratio Calculations 105 5.5 Selected Test Results 107 5.6 Sample Autocorrelation Theory 112 5.7 Random Walk Tests Using Rescaled Returns 115 5.8 Summary 120 Chapter 6: Further Tests of the Random Walk Hypothesis 121 6.1 Introduction 121 6.2 Test Methodology 122 6.3 Further Autocorrelation Tests 126 6.4 Spectral Tests 130 6.5 The Runs Test 133 6.6 Rescaled Range Tests 135 6.7 The BDS Test 136 6.8 Test Results for the Random Walk Hypothesis 138 6.9 The Size and Power of Random Walk Tests 144 6.10 Sources of Minor Dependence in Returns 148 6.11 Concluding Remarks 151 6.12 Appendix: the Correlation between Test Values for Two Correlated Series 153 6.13 Appendix: Autocorrelation Induced by Rescaling Returns 154 Chapter 7: Trading Rules and Market Efficiency 157 7.1 Introduction 157 7.2 Four Trading Rules 158 7.3 Measures of Return Predictability 163 7.4 Evidence about Equity Return Predictability 166 7.5 Evidence about the Predictability of Currency and Other Returns 168 7.6 An Example of Calculations for the Moving-Average Rule 172 7.7 Efficient Markets: Methodological Issues 175 7.8 Breakeven Costs for Trading Rules Applied to Equities 176 7.9 Trading Rule Performance for Futures Contracts 179 7.10 The Efficiency of Currency Markets 181 7.11 Theoretical Trading Profits for Autocorrelated Return Processes 184 7.12 Concluding Remarks 186 PART III: Volatility Processes 187 Chapter 8: An Introduction to Volatility 189 8.1 Definitions of Volatility 189 8.2 Explanations of Changes in Volatility 191 8.3 Volatility and Information Arrivals 193 8.4 Volatility and the Stylized Facts for Returns 195 8.5 Concluding Remarks 196 Chapter 9: ARCH Models: Definitions and Examples 197 9.1 Introduction 197 9.2 ARCH(1) 198 9.3 GARCH 1 1 199 9.4 An Exchange Rate Example of the GARCH 1 1 Model 205 9.5 A General ARCH Framework 212 9.6 Nonnormal Conditional Distributions 217 9.7 Asymmetric Volatility Models 220 9.8 Equity Examples of Asymmetric Volatility Models 222 9.9 Summary 233 Chapter 10: ARCH Models: Selection and Likelihood Methods 235 10.1 Introduction 235 10.2 Asymmetric Volatility: Further Specifications and Evidence 235 10.3 Long Memory ARCH Models 242 10.4 Likelihood Methods 245 10.5 Results from Hypothesis Tests 251 10.6 Model Building 256 10.7 Further Volatility Specifications 261 10.8 Concluding Remarks 264 10.9 Appendix: Formulae for the Score Vector 265 Chapter 11: Stochastic Volatility Models 267 11.1 Introduction 267 11.2 Motivation and Definitions 268 11.3 Moments of Independent SV Processes 270 11.4 Markov Chain Models for Volatility 271 11.5 The Standard Stochastic Volatility Model 278 11.6 Parameter Estimation for the Standard SV Model 283 11.7 An Example of SV Model Estimation for Exchange Rates 288 11.8 Independent SV Models with Heavy Tails 291 11.9 Asymmetric Stochastic Volatility Models 293 11.10 Long Memory SV Models 297 11.11 Multivariate Stochastic Volatility Models 298 11.12 ARCH versus SV 299 11.13 Concluding Remarks 301 11.14 Appendix: Filtering Equations 301 PART IV: High-Frequency Methods 303 Chapter 12: High-Frequency Data and Models 305 12.1 Introduction 305 12.2 High-Frequency Prices 306 12.3 One Day of High-Frequency Price Data 309 12.4 Stylized Facts for Intraday Returns 310 12.5 Intraday Volatility Patterns 316 12.6 Discrete-Time Intraday Volatility Models 321 12.7 Trading Rules and Intraday Prices 325 12.8 Realized Volatility: Theoretical Results 327 12.9 Realized Volatility: Empirical Results 332 12.10 Price Discovery 342 12.11 Durations 343 12.12 Extreme Price Changes 344 12.13 Daily High and Low Prices 346 12.14 Concluding Remarks 348 12.15 Appendix: Formulae for the Variance of the Realized Volatility Estimator 349 PART V: Inferences from Option Prices 351 Chapter 13: Continuous-Time Stochastic Processes 353 13.1 Introduction 353 13.2 The Wiener Process 354 13.3 Diffusion Processes 355 13.4 Bivariate Diffusion Processes 359 13.5 Jump Processes 361 13.6 Jump-Diffusion Processes 363 13.7 Appendix: a Construction of the Wiener Process 366 Chapter 14: Option Pricing Formulae 369 14.1 Introduction 369 14.2 Definitions, Notation, and Assumptions 370 14.3 Black-Scholes and Related Formulae 372 14.4 Implied Volatility 378 14.5 Option Prices when Volatility Is Stochastic 383 14.6 Closed-Form Stochastic Volatility Option Prices 388 14.7 Option Prices for ARCH Processes 391 14.8 Summary 394 14.9 Appendix: Heston's Option Pricing Formula 395 Chapter 15: Forecasting Volatility 397 15.1 Introduction 397 15.2 Forecasting Methodology 398 15.3 Two Measures of Forecast Accuracy 401 15.4 Historical Volatility Forecasts 403 15.5 Forecasts from Implied Volatilities 407 15.6 ARCH Forecasts that Incorporate Implied Volatilities 410 15.7 High-Frequency Forecasting Results 414 15.8 Concluding Remarks 420 Chapter 16: Density Prediction for Asset Prices 423 16.1 Introduction 423 16.2 Simulated Real-World Densities 424 16.3 Risk-Neutral Density Concepts and Definitions 428 16.4 Estimation of Implied Risk-Neutral Densities 431 16.5 Parametric Risk-Neutral Densities 435 16.6 Risk-Neutral Densities from Implied Volatility Functions 446 16.7 Nonparametric RND Methods 448 16.8 Towards Recommendations 450 16.9 From Risk-Neutral to Real-World Densities 451 16.10 An Excel Spreadsheet for Density Estimation 458 16.11 Risk Aversion and Rational RNDs 461 16.12 Tail Density Estimates 464 16.13 Concluding Remarks 465 Symbols 467 References 473 Author Index 503 Subject Index 513

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Book SynopsisOffers an introduction to the theoretical and methodological foundations of competitive asset pricing. This book develops the fundamentals of arbitrage pricing, mean-variance analysis, equilibrium pricing, and optimal consumption/portfolio choice in discrete settings, with emphasis on geometric and martingale methods.Trade Review"Costis Skiadas has hit a grand-slam with Asset Pricing Theory which fills a great void. It will speak to you in a well-designed, and thoughtful manner encouraging you to read a high-level and rigorous development of the subject regardless of your age, profession or position as economists, mathematicians, financial engineers, and physicists. I am adding it to my 'must read list' for my students and associates. I predict that Asset Pricing Theory will establish itself as a standard reference for many years to come, and this is the quality I admire--a quality that can only be born from experience. Read this book if you want to lead an organization, or lead the way."--Current Engineering Practice "I am sure any ambitious student who has read it will be drawn into the field immediately... I like the book very much and would recommend it for use in any serious asset pricing theory subject."--Qi Zeng, Economic RecordTable of ContentsPreface xi Notation and Conventions xv PART ONE: SINGLE-PERIOD ANALYSIS CHAPTER ONE: Financial Market and Arbitrage 3 1.1 Market and Arbitrage 3 1.2 Present Value and State Prices 6 1.3 Market Completeness and Dominant Choice 9 1.4 Probabilistic Representations of Value 12 1.5 Financial Contracts and Portfolios 15 1.6 Returns 17 1.7 Trading Constraints 19 1.8 Exercises 22 1.9 Notes 27 CHAPTER TWO: Mean-Variance Analysis 29 2.1 Market and Inner Product Structure 29 2.2 Minimum-Variance Cash Flows 32 2.3 Minimum-Variance Returns 35 2.4 Beta Pricing 37 2.5 Sharpe Ratios 40 2.6 Mean-Variance Efficiency 43 2.7 Factor Pricing 46 2.8 Exercises 49 2.9 Notes 54 CHAPTER THREE: Optimality and Equilibrium 55 3.1 Preferences, Optimality and State Prices 55 3.2 Equilibrium 58 3.3 Effective Market Completeness 62 3.4 Representative-Agent Pricing 65 3.4.1 Aggregation Based on Scale Invariance 66 3.4.2 Aggregation Based on Translation Invariance 69 3.5 Utility 71 3.5.1 Compensation Function Construction of Utilities 72 3.5.2 Additive Utilities 76 3.6 Utility and Individual Optimality 79 3.7 Utility and Allocational Optimality 83 3.8 Exercises 87 3.9 Notes 91 CHAPTER FOUR: Risk Aversion 94 4.1 Absolute and Comparative Risk Aversion 94 4.2 Expected Utility 99 4.3 Expected Utility and Risk Aversion 103 4.3.1 Comparative Risk Aversion 103 4.3.2 Absolute Risk Aversion 105 4.4 Risk Aversion and Simple Portfolio Choice 109 4.5 Coefficients of Risk Aversion 112 4.6 Simple Portfolio Choice for Small Risks 116 4.7 Stochastic Dominance 120 4.8 Exercises 124 4.9 Notes 129 PART TWO: DISCRETE DYNAMICS CHAPTER FIVE: Dynamic Arbitrage Pricing 135 5.1 Dynamic Market and Present Value 135 5.1.1 Time-Zero Market and Present-Value Functions 135 5.1.2 Dynamic Market and Present-Value Functions 138 5.2 Financial Contracts 142 5.2.1 Basic Arbitrage Restrictions and Trading Strategies 142 5.2.2 Budget Equations and Synthetic Contracts 146 5.3 Probabilistic Representations of Value 150 5.3.1 State-Price Densities 150 5.3.2 Equivalent Martingale Measures 154 5.4 Dominant Choice and Option Pricing 159 5.4.1 Dominant Choice 160 5.4.2 Recursive Value Maximization 164 5.4.3 Arbitrage Pricing of Options 166 5.5 State-Price Dynamics 170 5.6 Market Implementation 174 5.7 Markovian Pricing 178 5.8 Exercises 183 5.9 Notes 193 CHAPTER SIX: Dynamic Optimality and Equilibrium 195 6.1 Dynamic Utility 195 6.2 Expected Discounted Utility 199 6.3 Recursive Utility 202 6.4 Basic Properties of Recursive Utility 206 6.4.1 Comparative Risk Aversion 206 6.4.2 Utility Gradient Density 208 6.4.3 Concavity 211 6.5 Scale/Translation Invariance 213 6.5.1 Scale-Invariant Kreps-Porteus Utility 213 6.5.2 Translation-Invariant Kreps-Porteus Utility 217 6.6 Equilibrium Pricing 219 6.6.1 Intertemporal Marginal Rate of Substitution 220 6.6.2 State Pricing with SI Kreps-Porteus Utility 221 6.6.3 State Pricing with TI Kreps-Porteus Utility 227 6.7 Optimal Consumption and Portfolio Choice 229 6.7.1 Generalities 230 6.7.2 Scale-Invariant Formulation 232 6.7.3 Translation-Invariant Formulation 240 6.8 Exercises 248 6.9 Notes 252 PART THREE: MATHEMATICAL BACKGROUND APPENDIX A: Optimization Principles 259 A.1 Vector Space 259 A.2 Inner Product 261 A.3 Norm 264 A.4 Continuity 266 A.5 Compactness 268 A.6 Projections 270 A.7 Supporting Hyperplanes 274 A.8 Global Optimality Conditions 276 A.9 Local Optimality Conditions 278 A.10 Exercises 281 A.11 Notes 284 APPENDIX B: Discrete Stochastic Analysis 285 B.1 Events, Random Variables, Expectation 285 B.2 Algebras and Measurability 289 B.3 Conditional Expectation 292 B.4 Stochastic Independence 296 B.5 Filtration, Stopping Times and Stochastic Processes 299 B.6 Martingales 304 B.7 Predictable Martingale Representation 308 B.8 Change of Measure and Martingales 312 B.9 Markov Processes 317 B.10 Exercises 320 B.11 Notes 324 Bibliography 327 Index 341

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Book SynopsisEconomic forecasting involves choosing simple yet robust models to best approximate highly complex and evolving data-generating processes. This poses unique challenges for researchers in a host of practical forecasting situations, from forecasting budget deficits and assessing financial risk to predicting inflation and stock market returns. EconomiTrade Review"This book is an excellent and valuable one on economic forecasting for academics as well as practitioners. Specifically, the decision-theoretical approach employed by the book successfully conveys a new insight into the forecasting literature by making a clear connection between forecasting and decision-making. In addition, the book’s comprehensive arguments with numerous examples have no equal in other forecasting books."---Tatsuyoshi Okimoto, Economic Record

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Book SynopsisThe concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model.Trade Review"The economic concepts and differential topology methods presented in this book are clear, accessible and detailed so the reader can study the book independently without requiring any serious prior knowledge... [T]his comprehensive and pedagogical book is suitable for graduate students and also for researchers in this field."--Ioannis A. Polyrakis, Mathematical Reviews Clippings "General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field."--World Book IndustryTable of ContentsPreface xi CHAPTER 1: Goods and Prices 1 1.1 Introduction 1 1.2 Goods 1 1.3 Prices 2 1.4 Relative Prices 2 1.5 Price Normalization 3 1.6 Notes and Comments 4 CHAPTER 2: Preferences and Utility 5 2.1 Consumption Sets 5 2.2 Binary Relations 6 2.3 Consumers' Preferences 8 2.4 Smooth Utility Functions 14 2.5 Conclusion 18 2.6 Notes and Comments 18 CHAPTER 3: Demand Functions 19 3.1 Introduction 19 3.2 Constrained Utility Maximization 19 3.3 The Individual Demand Function 23 3.4 Properties of Demand Functions in D 24 3.5 Demand-based Consumer Theory 31 3.6 Conclusion 36 3.7 Notes and Comments 36 CHAPTER 4: The Exchange Model 37 4.1 Introduction 37 4.2 The Sets E, Er, and Ec of m-tuples of Demand Functions Defining the Exchange Model 38 4.3 The Exchange Model 39 4.4 Equilibrium Equation 39 4.5 The Equilibrium Manifold and the Natural Projection 41 4.6 The Smooth Equilibrium Manifold 42 4.7 Smoothness of the Natural Projection 44 4.8 Critical and Regular Points and Values 44 4.9 Notes and Comments 46 CHAPTER 5: The Equilibrium Manifold 47 5.1 Introduction 47 5.2 Global Properties and Their Interest 47 5.3 The No-trade Equilibria 49 5.4 The Fibers of the Equilibrium Manifold 50 5.5 The Equilibrium Manifold as a Collection of Linear Fibers Parameterized by the No-trade Equilibria 52 5.6 A Picture of the Equilibrium Manifold 53 5.7 Diffeomorphism with R_m 53 5.8 Conclusion 54 5.9 Notes and Comments 55 CHAPTER 6: Applications of the Global Coordinate System 56 6.1 Introduction 56 6.2 Coordinate System (A) 56 6.3 Coordinate System (B) 57 6.4 Formulas of the Natural Projection 57 6.5 The Jacobian Matrix of Aggregate Excess Demand 58 6.6 Conclusion 61 6.7 Notes and Comments 61 CHAPTER 7: The Broad Picture 62 7.1 Introduction 62 7.2 Properness 62 7.3 Smooth Selection at a Regular Equilibrium 63 7.4 The Equilibrium Manifold over Regular Economies 64 7.5 Genericity of Regular Economies 67 7.6 The Degrees of the Natural Projection 69 7.7 Conclusion 72 7.8 Notes and Comments 73 CHAPTER 8: The Fine Picture 74 8.1 Introduction 74 8.2 Aggregate Demand at a No-trade Equilibrium 74 8.3 Regularity of the No-trade Equilibria 75 8.4 The Set of Equilibrium Allocations 75 8.5 Economies with a Unique Equilibrium 78 8.6 Degree of the Natural Projection 79 8.7 The Set of Regular Equilibria 79 8.8 Conclusion 81 8.9 Notes and Comments 81 CHAPTER 9: Production with Decreasing Returns 82 9.1 Introduction 82 9.2 Production Sets: Definitions 82 9.3 Production Sets: Main Properties 84 9.4 The Firm's Objective Function 89 9.5 The Strict Decreasing Returns to Scale Firm 90 9.6 The Net Supply Function as a Primitive Concept 92 9.7 Conclusion 94 9.8 Notes and Comments 95 CHAPTER 10: Equilibrium with Decreasing Returns 96 10.1 Introduction 96 10.2 The General Equilibrium Model with Private Ownership of Decreasing Returns to Scale Firms 96 10.3 Production Adjusted Demand Functions 98 10.4 The Equivalent Exchange Model 101 10.5 Properness of the Natural Projection 103 10.6 Conclusion 107 10.7 Notes and Comments 107 CHAPTER 11: Production with Constant Returns 108 11.1 Introduction 108 11.2 Production Sets 109 11.3 The Net Supply Correspondence 112 11.4 Three Examples 115 11.5 Net Supply Correspondence of a Smooth Constant Returns to Scale Firm 118 11.6 The Graph of the Net Supply Correspondence 120 11.7 Conclusion 123 11.8 Notes and Comments 123 CHAPTER 12: Equilibrium with Constant Returns 124 12.1 Introduction 124 12.2 Decreasing and Constant Returns: General Case 124 12.3 Constant Returns: Reduced Form 125 12.4 Equilibria of the Model N 126 12.5 The Equilibrium Manifold Approach 126 12.6 The Equilibrium Manifold for the Model N 127 12.7 The Natural Projection 133 12.8 Regular and Critical Equilibria 134 12.9 Degrees of the Natural Projection 137 12.10 Regular and Singular Economies 138 12.11 Uniqueness of Equilibrium over ?(T) 139 12.12 The Natural Projection as a Finite Covering of the Set of Regular Economies 141 12.13 Values of the Natural Projection Degrees 143 12.14 Conclusion 144 12.15 Notes and Comments 144 Postscript 145 APPENDIX A: Notation 149 A.1 Points, Vectors, Inner Product 149 A.2 Gradient 149 A.3 Second-Order Derivatives and the Hessian Matrix of a Smooth Function 150 APPENDIX B: Point-set Topology 151 B.1 Proper Maps 151 APPENDIX C: Smooth Manifolds 152 C.1 The Implicit Function Theorem 152 C.2 Smooth Manifolds and Submanifolds 152 C.3 Smooth Mappings, Immersions, and Submersions 153 APPENDIX D: Singularities of Smooth Maps 155 D.1 Critical and Regular Points 155 D.2 Singular and Regular Values 155 D.3 Sard's Theorem 156 D.4 The Regular Value Theorem 156 D.5 The Case where dimX = dimY 156 D.6 Coverings 157 D.7 Surjectivity of Maps with Non-Zero Modulo 2 Degree 157 APPENDIX E: Convexity 159 E.1 Convex and Strictly Convex Sets 159 E.2 Quasi-concave Functions 159 E.3 Smooth Quasi-concavity and Second-Order Derivatives 162 E.4 Bordered Hessian of a Smoothly Quasi-concave Function 164 E.5 Recession Cone of a Convex Set 165 APPENDIX F: Miscellany 166 F.1 Dimension of Semi-algebraic Sets 166 References 167 Index 171

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Book SynopsisProvides an overview and exploration of methodologies, models, and techniques used to analyze forces shaping national economies. This title presents a range of methods for characterizing and evaluating empirical implications, including calibration exercises, method-of-moment procedures, and likelihood-based procedures, both classical and Bayesian.Trade Review"Structural Macroeconometrics is the ideal textbook for graduate students seeking an introduction to macroeconomics and econometrics, and for advanced students pursuing applied research in macroeconomics. The book's historical perspective, along with its broad presentation of alternative methodologies, makes it an indispensable resource for academics and professionals."--World Book IndustryTable of ContentsPreface xiii Preface to the First Edition xv Part I Introduction Chapter 1: Background and Overview 3 1.1 Background 3 1.2 Overview 4 Chapter 2: Casting Models in Canonical Form 9 2.1 Notation 9 2.1.1 Log-Linear Model Representations 11 2.1.2 Nonlinear Model Representations 11 2.2 Linearization 12 2.2.1 Taylor Series Approximation 12 2.2.2 Log-Linear Approximations 14 2.2.3 Example Equations 15 Chapter 3: DSGE Models: Three Examples 18 3.1 Model I: A Real Business Cycle Model 20 3.1.1 Environment 20 3.1.2 The Nonlinear System 23 3.1.3 Log-Linearization 26 3.2 Model II: Monopolistic Competition and Monetary Policy 28 3.2.1 Environment 28 3.2.2 The Nonlinear System 33 3.2.3 Log-Linearization 34 3.3 Model III: Asset Pricing 38 3.3.1 Single-Asset Environment 38 3.3.2 Multi-Asset Environment 39 3.3.3 Alternative Preference Specifications 40 Part II Model Solution Techniques Chapter 4: Linear Solution Techniques 51 4.1 Homogeneous Systems 52 4.2 Example Models 54 4.2.1 The Optimal Consumption Model 54 4.2.2 Asset Pricing with Linear Utility 55 4.2.3 Ramsey's Optimal Growth Model 56 4.3 Blanchard and Kahn's Method 57 4.4 Sims' Method 61 4.5 Klein's Method 64 4.6 An Undetermined Coefficients Approach 66v Chpater 5: Nonlinear Solution Techniques 69 5.1 Projection Methods 71 5.1.1 Overview 71 5.1.2 Finite Element Methods 72 5.1.3 Orthogonal Polynomials 73 5.1.4 Implementation 74 5.1.5 Extension to the l-dimensional Case 78 5.1.6 Application to the Optimal Growth Model 79 5.2 Iteration Techniques: Value-Function and Policy-Function Iterations 87 5.2.1 Dynamic Programming 87 5.2.2 Value-Function Iterations 89 5.2.3 Policy-Function Iterations 94 5.3 Perturbation Techniques 95 5.3.1 Notation 95 5.3.2 Overview 97 5.3.3 Application to DSGE Models 99 5.3.4 Application to an Asset-Pricing Model 105 Part III Data Preparation and Representation Chapter 6: Removing Trends and Isolating Cycles 113 6.1 Removing Trends 115 6.2 Isolating Cycles 120 6.2.1 Mathematical Background 120 6.2.2 Cramer Representations 124 6.2.3 Spectra 125 6.2.4 Using Filters to Isolate Cycles 126 6.2.5 The Hodrick-Prescott Filter 128 6.2.6 Seasonal Adjustment 130 6.2.7 Band Pass Filters 131 6.3 Spuriousness 134 Chapter 7: Summarizing Time Series Behavior When All Variables Are Observable 138 7.1 Two Useful Reduced-Form Models 139 7.1.1 The ARMA Model 139 7.1.2 Allowing for Heteroskedastic Innovations 145 7.1.3 The VAR Model 147 7.2 Summary Statistics 149 7.2.1 Determining Lag Lengths 157 7.2.2 Characterizing the Precision of Measurements 159 7.3 Obtaining Theoretical Predictions of Summary Statistics 162 Chapter 8: State-Space Representations 166 8.1 Introduction 166 8.1.1 ARMA Models 167 8.2 DSGE Models as State-Space Representations 169 8.3 Overview of Likelihood Evaluation and Filtering 171 8.4 The Kalman Filter 173 8.4.1 Background 173 8.4.2 The Sequential Algorithm 175 8.4.3 Smoothing 178 8.4.4 Serially Correlated Measurement Errors 181 8.5 Examples of Reduced-Form State-Space Representations 182 8.5.1 Time-Varying Parameters 182 8.5.2 Stochastic Volatility 185 8.5.3 Regime Switching 186 8.5.4 Dynamic Factor Models 187 Part IV Monte Carlo Methods Chapter 9: Monte Carlo Integration: The Basics 193 9.1 Motivation and Overview 193 9.2 Direct Monte Carlo Integration 196 9.2.1 Model Simulation 198 9.2.2 Posterior Inference via Direct Monte Carlo Integration 201 9.3 Importance Sampling 202 9.3.1 Achieving Efficiency: A First Pass 206 9.4 Efficient Importance Sampling 211 9.5 Markov Chain Monte Carlo Integration 215 9.5.1 The Gibbs Sampler 216 9.5.2 Metropolis-Hastings Algorithms 218 Chapter 10: Likelihood Evaluation and Filtering in State-Space Representations Using Sequential Monte Carlo Methods 221 10.1 Background 221 10.2 Unadapted Filters 224 10.3 Conditionally Optimal Filters 228 10.4 Unconditional Optimality: The EIS Filter 233 10.4.1 Degenerate Transitions 235 10.4.2 Initializing the Importance Sampler 236 10.4.3 Example 239 10.5 Application to DSGE Models 241 10.5.1 Initializing the Importance Sampler 243 10.5.2 Initializing the Filtering Density 245 10.5.3 Application to the RBC Model 246 Part V Empirical Methods Chapter 11: Calibration 253 11.1 Historical Origins and Philosophy 253 11.2 Implementation 258 11.3 The Welfare Cost of Business Cycles 261 11.4 Productivity Shocks and Business Cycle Fluctuations 268 11.5 The Equity Premium Puzzle 273 11.6 Critiques and Extensions 276 11.6.1 Critiques 276 11.6.2 Extensions 279 Chapter 12: Matching Moments 285 12.1 Overview 285 12.2 Implementation 286 12.2.1 The Generalized Method of Moments 286 12.2.2 The Simulated Method of Moments 294 12.2.3 Indirect Inference 297 12.3 Implementation in DSGE Models 300 12.3.1 Analyzing Euler Equations 300 12.3.2 Analytical Calculations Based on Linearized Models 301 12.3.3 Simulations Involving Linearized Models 306 12.3.4 Simulations Involving Nonlinear Approximations 307 12.4 Empirical Application: Matching RBC Moments 308 Chapter 13: Maximum Likelihood 314 13.1 Overview 314 13.2 Introduction and Historical Background 316 13.3 A Primer on Optimization Algorithms 318 13.3.1 Simplex Methods 319 13.3.2 Derivative-Based Methods 328 13.4 Ill-Behaved Likelihood Surfaces: Problems and Solutions 330 13.4.1 Problems 330 13.4.2 Solutions 331 13.5 Model Diagnostics and Parameter Stability 334 13.6 Empirical Application: Identifying Sources of Business Cycle Fluctuations 337 Chapter 14: Bayesian Methods 351 14.1 Overview of Objectives 351 14.2 Preliminaries 352 14.3 Using Structural Models as Sources of Prior Information for Reduced-Form Analysis 355 14.4 Implementing Structural Models Directly 360 14.5 Model Comparison 361 14.6 Using an RBC Model as a Source of Prior Information for Forecasting 364 14.7 Estimating and Comparing Asset-Pricing Models 373 14.7.1 Estimates 380 14.7.2 Model Comparison 384 References 387 Index 401

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Book SynopsisTrade Review"The authors’ focused and practical approach manages to make demanding mathematical tools and continuous-time stochastic methods accessible to a wide audience, without sacrificing mathematical rigor."---Andrianos E. Tsekrekos, Journal of Economics

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Book SynopsisTrade Review"Lars Peter Hansen, Co-Winner of the 2013 Nobel Prize in Economics""Thomas J. Sargent, Winner of the 2011 Nobel Prize in Economics""This book is chock full of results that will be useful to all interested in dynamic linear models, including material that will be novel to even the experienced macroeconomist. Buy it, read it, use it."---Kenneth D. West, Journal of Economic Literature

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Book SynopsisOne of the most urgent challenges in African economic development is to devise a strategy for improving statistical capacity. Reliable statistics, including estimates of economic growth rates and per-capita income, are basic to the operation of governments in developing countries and vital to nongovernmental organizations and other entities that provide financial aid to them. Rich countries and international financial institutions such as the World Bank allocate their development resources on the basis of such data. The paucity of accurate statistics is not merely a technical problem; it has a massive impact on the welfare of citizens in developing countries.Where do these statistics originate? How accurate are they? Poor Numbers is the first analysis of the production and use of African economic development statistics. Morten Jerven's research shows how the statistical capacities of sub-Saharan African economies have fallen into disarray. The numbers substantially misstate tTrade Review[Poor Numbers]is a useful reminder of the dubious information content of economic indicators generated by national accounting systems of sub-Saharan African states. I recommend the book to all scholars and researchers who contemplate the use of data generated by national accounting systems of sub-Saharan African countries. * Quarterly Journal of International Agriculture *The book is remarkable given that it is largely the result of the efforts of a single individual gaining access to NSOs.... Highly recommended to all those interested in the SSA region and in the measurement of economic activity in developing countries. Its publication has already started a much-needed lively discussion, which is a precondition for improving the quality of macro-economic statistics. * The Africa Policy Journal at the Harvard Kennedy School *Poor Numbers is a powerful little book..., highlighting the risks of making political inferences solely based on statistical analysis...Although an economist by training, Jerven's clear prose without jargon helps make Poor Numbers reach a wider readership. It is imperative to note that his is not a simple criticism of quantitative methodology, but of the confidence one has in the findings of quantitative analysis without due attention to the quality of the data. In this sense, even those who have no scholarly interest in African development economics would find the findings and conclusions pertinent to the foundational debates on the role of methodology and theory in political science. * European Political Science *"Increasingly, scientists turn to the large statistical databases of international bodies when testing favoured hypotheses to control for growth and economic development. They might hesitate after reading Poor Numbers.... This book offers fascinating, disturbing insights for anyone interested in the role of numbers in the social sciences. For those using global economic databases, it should be required reading." * Nature *This important book attempts to systematize what most quantitative practitioners in Africa generally understand: African macroeconomic data are poor.... Using a variety of sources that include current surveys of in-country statistical collection agencies and firsthand historical accounts, Jerven outlines several root causes of the data problem, which include Africa's colonial heritage and the more recent, structural adjustment policies. He continues his analysis by exploring how data are consciously shaped by both local and international politics and international aid agencies. Specifically, Jerven is critical of World Bank transparency and its unwillingness to provide him with quantitative methodologies of its official data compilation.... This volume opens up a venue for a research paradigm that could lead to much-needed improvements in the collection of African data. Summing Up: Highly recommended. * Choice *Table of ContentsIntroduction1. What Do We Know about Income and Growth in Africa?2. Measuring African Wealth and Progress3. Facts, Assumptions, and Controversy: Lessons from the Datasets4. Data for Development: Using and Improving African StatisticsConclusion: Development by NumbersAppendix A. A Comparison of GDP Estimates from the World Development Indicators Database and Country EstimatesAppendix B. Details of Interviews and QuestionnairesNotes References Index

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Book SynopsisThe book offers an eclectic treatment of the human capital-economic growth nexus and uses state-of-the-art nonlinear econometric methods to provide an empirical assessment of the link between human capital and economic growth.Trade Review"The authors provide an in-depth investigation of the link between human capital and economic growth. They take an innovative approach, examining the determinants of economic growth through a historical overview of the concept of human capital." —Abstracts of Public Administration, Development, and Environment"This book imparts a deep understanding of the nexus between human capital and aggregate economic growth. By studying this book, you will have not only acquired the specific human capital knowledge to participate in the literature on human capital and growth, but will also have acquired general human capital knowledge that will improve your productivity in other economic areas." —Merwan H. Engineer, University of Victoria"The authors are excellent writers and experts on the topics they cover in this volume. They use an array of results to make the case that, indeed, human capital affects growth in a highly nonlinear way. There is nothing that is as extensive on the issue of human capital and economic growth as this book."—Chris Papageorgiou, Research Department of the International Monetary FundTable of ContentsPART I Introduction 1 Introduction to Human Capital and Economic 3 Growth 2 The Concept of Human Capital: A Brief 10 Historical Review PARTII Theoretical Research on Human Capital and Economic Growth 3 Theoretical Models of Human Capital and 27 Economic Growth 4 Human Capital and Endogenous Models of 53 Economic Growth 5 Threshold Effects, Multiple Equilibria, and 84 Nonlinearities in Human Capital and Economic Growth PARTIII The Empirics of Human Capital and Economic Growth 6 Empirical Studies on Human Capital and 107 Economic Growth 7 Human Capital and Economic Growth: Linear 156 Specifications 8 A Primer on Nonparametric Methods and Their 172 Application to Research in Human Capital and Economic Growth 9 Human Capital and Economic Growth: 193 Nonlinear Specifications Appendix: Nonparametric Methods 211 Glossary 217 Bibliography 221

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Book SynopsisWritten in a comprehensive yet accessible style, this Handbook introduces readers to a range of modern empirical methods with applications in microeconomics, illustrating how to use two of the most popular software packages, Stata and R, in microeconometric applications.Table of ContentsContents: Introduction to the Handbook of Research Methods and Applications in Empirical Microeconomics ix Nigar Hashimzade and Michael A. Thornton PART I ECONOMETRIC METHODS IN MICROECONOMICS 1 Linear dynamic panel data models 2 Ryo Okui 2 Spatial autoregressive nonlinear models in R with an empirical application in labour economics 23 Anna Gloria Billé 3 Econometric analyses of auctions: a selective review 42 Tong Li and Xiaoyong Zheng 4 An introduction to flexible methods for policy evaluation 82 Martin Huber PART II HOUSEHOLDS, BUSINESSES AND SOCIETIES 5 Econometric models of fertility 113 Alfonso Miranda and Pravin K. Trivedi 6 Measuring discrimination in the labour market 155 Emmanuel Duguet 7 Microeconomic models for designing and evaluating tax-transfer systems 195 Ugo Colombino 8 Bounds on counterfactuals in semiparametric discrete-choice models 223 Khai X. Chiong, Yu-Wei Hsieh and Matthew Shum 9 Bank performance analysis 238 Natalya Zelenyuk and Valentin Zelenyuk 10 Empirical methods in social epidemiology 280 Christopher F. Baum PART III POLICY EVALUATION AND CAUSALITY 11 Policy evaluation using causal inference methods 294 Denis Fougère and Nicolas Jacquemet 12 Regression discontinuity designs in policy evaluation 325 Otávio Bartalotti, Marinho Bertanha and Sebastian Calonico 13 Measuring the effect of health events in the labour market 359 Emmanuel Duguet PART IV NETWORKS AND BIG DATA IN MICROECONOMICS 14 Exploring social media: Twitteronomics and beyond 388 Tho Pham, Piotr Śpiewanowski and Oleksandr Talavera 15 Econometrics of networks with limited access to network data: a literature survey 416 Pedro C.L. Souza 16 Machine learning for causal inference: estimating heterogeneous treatment effects 438 Vishalie Shah, Noemi Kreif and Andrew M. Jones PART V STATA AND R IN MICROECONOMETRIC APPLICATIONS 17 Stochastic frontier analysis in Stata: using existing and coding new commands 489 Oleg Badunenko 18 Modern R workflow and tools for microeconometric data analysis 518 Giovanni Baiocchi 19 Robust inference in panel data microeconometrics, using R 564 Giovanni Millo 20 Econometric estimation of the “Constant Elasticity of Substitution” function in R: the micEconCES package 596 Arne Henningsen, Géraldine Henningsen and Gergő Literáti Index 641

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Book SynopsisReflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: Contributions by well-knownTable of ContentsNotes on Contributors xiii Preface xv 1 Trends and Trades 1Michael Carlisle, Olympia Hadjiliadis, and Ioannis Stamos 1.1 Introduction 1 1.2 A trend-based trading strategy 3 1.2.1 Signaling and trends 3 1.2.2 Gain over a subperiod 5 1.3 CUSUM timing 7 1.3.1 Cusum process and stopping time 7 1.3.2 A CUSUM timing scheme 10 1.3.3 US treasury notes, CUSUM timing 11 1.4 Example: Random walk on ticks 12 1.4.1 Random walk expected gain over a subperiod 15 1.4.2 Simple random walk, CUSUM timing 18 1.4.3 Lazy simple random walk, cusum timing 21 1.5 CUSUM strategy Monte Carlo 24 1.6 The effect of the threshold parameter 27 1.7 Conclusions and future work 39 Appendix: Tables 40 References 47 2 Gaussian Inequalities and Tranche Sensitivities 51Claas Becker and Ambar N. Sengupta 2.1 Introduction 51 2.2 The tranche loss function 52 2.3 A sensitivity identity 54 2.4 Correlation sensitivities 55 Acknowledgment 58 References 58 3 A Nonlinear Lead Lag Dependence Analysis of Energy Futures: Oil, Coal, and Natural Gas 61Germán G. Creamer and Bernardo Creamer 3.1 Introduction 61 3.1.1 Causality analysis 62 3.2 Data 64 3.3 Estimation techniques 64 3.4 Results 65 3.5 Discussion 67 3.6 Conclusions 69 Acknowledgments 69 References 70 4 Portfolio Optimization: Applications in Quantum Computing 73Michael Marzec 4.1 Introduction 73 4.2 Background 75 4.2.1 Portfolios and optimization 76 4.2.2 Algorithmic complexity 77 4.2.3 Performance 78 4.2.4 Ising model 79 4.2.5 Adiabatic quantum computing 79 4.3 The models 80 4.3.1 Financial model 81 4.3.2 Graph-theoretic combinatorial optimization models 82 4.3.3 Ising and Qubo models 83 4.3.4 Mixed models 84 4.4 Methods 84 4.4.1 Model implementation 85 4.4.2 Input data 85 4.4.3 Mean-variance calculations 85 4.4.4 Implementing the risk measure 86 4.4.5 Implementation mapping 86 4.5 Results 88 4.5.1 The simple correlation model 88 4.5.2 The restricted minimum-risk model 91 4.5.3 The WMIS minimum-risk, max return model 94 4.6 Discussion 95 4.6.1 Hardware limitations 97 4.6.2 Model limitations 97 4.6.3 Implementation limitations 98 4.6.4 Future research 98 4.7 Conclusion 100 Acknowledgments 100 Appendix 4.A: WMIS Matlab Code 100 References 103 5 Estimation Procedure for Regime Switching Stochastic Volatility Model and Its Applications 107Ionut Florescu and Forrest Levin 5.1 Introduction 107 5.1.1 The original motivation 108 5.1.2 The model and the problem 108 5.1.3 A brief historical note 109 5.2 The methodology 110 5.2.1 Obtaining filtered empirical distributions at t1,…, tT 110 5.2.2 Obtaining the parameters of the Markov chain 112 5.3 Results obtained applying the model to real data 113 5.3.1 Part i: financial applications 113 5.3.2 Part ii: physical data application. temperature data 119 5.3.3 Part iii: analysis of seismometer readings during an earthquake 121 5.3.4 Analysis of the earthquake signal: beginning 123 5.3.5 Analysis: during the earthquake 125 5.3.6 Analysis: end of the earthquake signal, aftershocks 127 5.4 Conclusion 127 5.A Theoretical results and empirical testing 128 5.A.1 How does the particle filter work? 128 5.A.2 Theoretical results about convergence and parameter estimates 129 5.A.3 Markov chain parameter estimates 131 5.A.4 Empirical testing 132 5.A.5 A list of supplementary documents 133 References 133 6 Detecting Jumps in High-Frequency Prices Under Stochastic Volatility: A Review and a Data-Driven Approach 137Ping-Chen Tsai and Mark B. Shackleton 6.1 Introduction 137 6.2 Review on the intraday jump tests 140 6.2.1 Realized volatility measure and the BNS tests 140 6.2.2 The ABD and LM tests 142 6.3 A data-driven testing procedure 146 6.3.1 Spy data and microstructure noise 146 6.3.2 A generalized testing procedure 149 6.4 Simulation study 153 6.4.1 Model specification 153 6.4.2 Simulation results 158 6.5 Empirical results 161 6.5.1 Results on the backward-looking test 162 6.5.2 Results on the interpolated test 165 6.6 Conclusion 165 Acknowledgments 166 Appendix 6.A: Least-square estimation of HAR-MA (2) model for log(BP) of SPY 167 Appendix 6.B: Estimation of ARMA (2, 1) model for log(BP) of SPY 168 Appendix 6.C: Minimized loss function loss(𝜌1, 𝜌2) for SV2FJ_2𝜌 model, SPY 169 Appendix 6.D.1: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.08 170 Appendix 6.D.2: Calibration of 𝜉 under SV2FJ_2𝜌 model at 2-min frequency, E[Nt] = 0.40 171 Appendix 6.D.3: Calibration of 𝜉 under SV2FJ_2𝜌 model at 5-min frequency, E[Nt] = 0.08 172 Appendix 6.D.4: Calibration of 𝜉 under SV2FJ_2𝜌 Model at 5-min frequency, E[Nt] = 0.40 173 Appendix 6.D.5: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.08 174 Appendix 6.D.6: Calibration of 𝜉 under SV2FJ_2𝜌 model at 10-min frequency, E[Nt] = 0.40 175 References 175 7 Hawkes Processes and Their Applications to High-Frequency Data Modeling 183Baron Law and Frederi G. Viens 7.1 Introduction 183 7.2 Point processes 184 7.3 Hawkes processes 186 7.3.1 Branching structure representation 188 7.3.2 Stationarity 188 7.3.3 Convergence 189 7.4 Statistical inference of Hawkes processes 191 7.4.1 Simulation 191 7.4.2 Estimation 194 7.4.3 Hypothesis testing 197 7.5 Applications of Hawkes processes 198 7.5.1 Modeling order arrivals 199 7.5.2 Modeling price jumps 200 7.5.3 Modeling jump-diffusion 205 7.5.4 Measuring endogeneity (Reflexivity) 205 Appendix 7.A: Point Processes 207 7.A.1 Definition 207 7.A.2 Moments 208 7.A.3 Marked point processes 209 7.A.4 Stochastic intensity 209 7.A.5 Random time change 211 Appendix 7.B: A Brief History of Hawkes processes 211 References 212 8 Multifractal Random Walk Driven by a Hermite Process 221Alexis Fauth and Ciprian A. Tudor 8.1 Introduction 221 8.2 Preliminaries 224 8.2.1 Fractional brownian motion and hermite processes 224 8.2.2 Wiener integrals with respect to the hermite process 226 8.2.3 Infinitely divisible cascading noise 229 8.3 Multifractal random walk driven by a Hermite process 231 8.3.1 Definition and existence 231 8.3.2 Properties of the hermite multifractal random walk 233 8.4 Financial applications 234 8.4.1 Simulation of the Hmrw 235 8.4.2 Financial statistics 241 8.5 Concluding remarks 243 References 247 9 Interpolating Techniques and Nonparametric Regression Methods Applied to Geophysical and Financial Data Analysis 251K. Basu and Maria C. Mariani 9.1 Introduction 251 9.2 Nonparametric regression models 253 9.2.1 Local polynomial regression 255 9.2.2 Lowess/loess method 257 9.2.3 Numerical applications 259 9.3 Interpolation methods 271 9.3.1 Nearest-neighbor interpolation 271 9.3.2 Bilinear interpolation 272 9.3.3 Bicubic interpolation 276 9.3.4 Biharmonic interpolation 277 9.3.5 Thin plate splines 282 9.3.6 Numerical applications 285 9.4 Conclusion 287 Acknowledgments 292 References 292 10 Study of Volatility Structures in Geophysics and Finance Using Garch Models 295Maria C. Mariani, F. Biney, and I. SenGupta 10.1 Introduction 295 10.2 Short memory models 297 10.2.1 ARMA(p,q) model 297 10.2.2 GARCH(p,q) model 297 10.2.3 IGARCH(1,1) model 298 10.3 Long memory models 298 10.3.1 ARFIMA(p,d,q) model 299 10.3.2 ARFIMA(p,d,q)-GARCH(r,s) 299 10.3.3 Intermediate memory process 300 10.3.4 Figarch model 300 10.4 Detection and estimation of long memory 302 10.4.1 Augmented dickey–fuller test(ADF test) 302 10.4.2 KPSS test 303 10.4.3 Whittle method 304 10.5 Data collection, analysis, and result 306 10.5.1 Analysis on dow Jones index (DJIA) returns 306 10.5.2 Model selection and specification: conditional mean 306 10.5.3 Conditional mean model (returns) 309 10.5.4 Model diagnostics: ARMA(2, 2) 309 10.5.5 Test for ARCH effect 311 10.5.6 Model selection and specification: Conditional variance 313 10.5.7 Standardized residuals test 314 10.5.8 Model diagnostics 314 10.5.9 Returns and variance equation 315 10.5.10 standardized residuals test 317 10.5.11 Model diagnostic of conditional returns with conditional variance 318 10.5.12 One-step ahead prediction of last 10 observations 330 10.5.13 Analysis on high-frequency, earthquake, and explosives series 330 10.6 Discussion and conclusion 335 References 337 11 Scale Invariance and Lévy Models Applied to Earthquakes and Financial High-Frequency Data 341M. P. Beccar-Varela, Ionut Florescu, and I. SenGupta 11.1 Introduction 341 11.2 Governing equations for the deterministic model 342 11.2.1 Application to geophysical (earthquake data) 343 11.2.2 Results 344 11.3 L´evy flights and application to geophysics 345 11.3.1 Truncated L´evy flight distribution 353 11.3.2 Results 356 11.4 Application to the high-frequency market data 360 11.4.1 Methodology 360 11.4.2 Results 361 11.5 Brief program code description 362 11.6 Conclusion 364 11.A Appendix 366 11.A.1 Stable distributions 366 11.A.2 Characterization of stable distributions 367 References 368 12 Analysis of Generic Diversity in the Fossil Record, Earthquake Series, and High-Frequency Financial Data 371M. P. Beccar Varela, F. Biney, Maria C. Mariani, I. SenGupta, M. Shpak, and P. Bezdek 12.1 Introduction 371 12.2 Statistical preliminaries and results 373 12.2.1 Sum of exponential random variables with different parameters 374 12.3 Statistical and numerical analysis 377 12.4 Analysis with Lévy distribution 380 12.4.1 Characterization of Stable Distributions 383 12.4.2 Truncated Lévy flight (TLF) distribution 384 12.4.3 Data analysis with TLF distribution 389 12.4.4 Sum of Lévy random variables with different parameters 390 12.5 Analysis of the Stock Indices, high-frequency (tick) data, and explosive series 394 12.6 Results and discussion 409 Acknowledgments 421 12.A Appendix A—Big ‘O’ notation 421 References 422 Index 425

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Book SynopsisApplied Econometric Time Series, 4th Edition demonstrates modern techniques for developing models capable of forecasting, interpreting, and testing hypotheses concerning economic data. In this text, Dr.Table of ContentsChapter 1: Difference Equations Chapter 2: Stationary Time-Series Models Chapter 3: Modeling Volatility Chapter 4: Models with Trend Chapter 5: Multiequation Time-Series Models Chapter 6: Cointegration and Error-Correction Models Chapter 7: Nonlinear Models and Breaks Index

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Book SynopsisReflects the developments and new directions in the field since the publication of the first successful edition and contains a complete set of problems and solutions This revised and expanded edition reflects the developments and new directions in the field since the publication of the first edition. In particular, sections on nonstationary panel data analysis and a discussion on the distinction between deterministic and stochastic trends have been added. Three new chapters on long-memory discrete-time and continuous-time processes have also been created, whereas some chapters have been merged and some sections deleted. The first eleven chapters of the first edition have been compressed into ten chapters, with a chapter on nonstationary panel added and located under Part I: Analysis of Non-fractional Time Series. Chapters 12 to 14 have been newly written under Part II: Analysis of Fractional Time Series. Chapter 12 discusses the basic theory of long-memory processes byTable of ContentsPreface to the Second Edition xi Preface to the First Edition xiii Part I Analysis of Non Fractional Time Series 1 1 Models for Nonstationarity and Noninvertibility 3 1.1 Statistics from the One-Dimensional Random Walk 3 1.1.1 Eigenvalue Approach 4 1.1.2 Stochastic Process Approach 11 1.1.3 The Fredholm Approach 12 1.1.4 An Overview of the Three Approaches 14 1.2 A Test Statistic from a Noninvertible Moving Average Model 16 1.3 The AR Unit Root Distribution 23 1.4 Various Statistics from the Two-Dimensional Random Walk 29 1.5 Statistics from the Cointegrated Process 41 1.6 Panel Unit Root Tests 47 2 Brownian Motion and Functional Central Limit Theorems 51 2.1 The Space L2 of Stochastic Processes 51 2.2 The Brownian Motion 55 2.3 Mean Square Integration 58 2.3.1 The Mean Square Riemann Integral 59 2.3.2 The Mean Square Riemann–Stieltjes Integral 62 2.3.3 The Mean Square Ito Integral 66 2.4 The Ito Calculus 72 2.5 Weak Convergence of Stochastic Processes 77 2.6 The Functional Central Limit Theorem 81 2.7 FCLT for Linear Processes 87 2.8 FCLT for Martingale Differences 91 2.9 Weak Convergence to the Integrated Brownian Motion 99 2.10 Weak Convergence to the Ornstein–Uhlenbeck Process 103 2.11 Weak Convergence of Vector-Valued Stochastic Processes 109 2.11.1 Space Cq 109 2.11.2 Basic FCLT for Vector Processes 110 2.11.3 FCLT for Martingale Differences 112 2.11.4 FCLT for the Vector-Valued Integrated Brownian Motion 115 2.12 Weak Convergence to the Ito Integral 118 3 The Stochastic Process Approach 127 3.1 Girsanov’s Theorem: O-U Processes 127 3.2 Girsanov’s Theorem: Integrated Brownian Motion 137 3.3 Girsanov’s Theorem: Vector-Valued Brownian Motion 142 3.4 The Cameron–Martin Formula 145 3.5 Advantages and Disadvantages of the Present Approach 147 4 The Fredholm Approach 149 4.1 Motivating Examples 149 4.2 The Fredholm Theory: The Homogeneous Case 155 4.3 The c.f. of the Quadratic Brownian Functional 161 4.4 Various Fredholm Determinants 171 4.5 The Fredholm Theory: The Nonhomogeneous Case 190 4.5.1 Computation of the Resolvent – Case 1 192 4.5.2 Computation of the Resolvent – Case 2 199 4.6 Weak Convergence of Quadratic Forms 203 5 Numerical Integration 213 5.1 Introduction 213 5.2 Numerical Integration: The Nonnegative Case 214 5.3 Numerical Integration: The Oscillating Case 220 5.4 Numerical Integration: The General Case 228 5.5 Computation of Percent Points 236 5.6 The Saddlepoint Approximation 240 6 Estimation Problems in Nonstationary Autoregressive Models 245 6.1 Nonstationary Autoregressive Models 245 6.2 Convergence in Distribution of LSEs 250 6.2.1 Model A 251 6.2.2 Model B 253 6.2.3 Model C 255 6.2.4 Model D 257 6.3 The c.f.s for the Limiting Distributions of LSEs 260 6.3.1 The Fixed Initial Value Case 261 6.3.2 The Stationary Case 265 6.4 Tables and Figures of Limiting Distributions 267 6.5 Approximations to the Distributions of the LSEs 276 6.6 Nearly Nonstationary Seasonal AR Models 281 6.7 Continuous Record Asymptotics 289 6.8 Complex Roots on the Unit Circle 292 6.9 Autoregressive Models with Multiple Unit Roots 300 7 Estimation Problems in Noninvertible Moving Average Models 311 7.1 Noninvertible Moving Average Models 311 7.2 The Local MLE in the Stationary Case 314 7.3 The Local MLE in the Conditional Case 325 7.4 Noninvertible Seasonal Models 330 7.4.1 The Stationary Case 331 7.4.2 The Conditional Case 333 7.4.3 Continuous Record Asymptotics 335 7.5 The Pseudolocal MLE 337 7.5.1 The Stationary Case 337 7.5.2 The Conditional Case 339 7.6 Probability of the Local MLE at Unity 341 7.7 The Relationship with the State Space Model 343 8 Unit Root Tests in Autoregressive Models 349 8.1 Introduction 349 8.2 Optimal Tests 350 8.2.1 The LBI Test 352 8.2.2 The LBIU Test 353 8.3 Equivalence of the LM Test with the LBI or LBIU Test 356 8.3.1 Equivalence with the LBI Test 356 8.3.2 Equivalence with the LBIU Test 358 8.4 Various Unit Root Tests 360 8.5 Integral Expressions for the Limiting Powers 362 8.5.1 Model A 363 8.5.2 Model B 364 8.5.3 Model C 365 8.5.4 Model D 367 8.6 Limiting Power Envelopes and Point Optimal Tests 369 8.7 Computation of the Limiting Powers 372 8.8 Seasonal Unit Root Tests 382 8.9 Unit Root Tests in the Dependent Case 389 8.10 The Unit Root Testing Problem Revisited 395 8.11 Unit Root Tests with Structural Breaks 398 8.12 Stochastic Trends Versus Deterministic Trends 402 8.12.1 Case of Integrated Processes 403 8.12.2 Case of Near-Integrated Processes 406 8.12.3 Some Simulations 409 9 Unit Root Tests in Moving Average Models 415 9.1 Introduction 415 9.2 The LBI and LBIU Tests 416 9.2.1 The Conditional Case 417 9.2.2 The Stationary Case 419 9.3 The Relationship with the Test Statistics in Differenced Form 424 9.4 Performance of the LBI and LBIU Tests 427 9.4.1 The Conditional Case 427 9.4.2 The Stationary Case 430 9.5 Seasonal Unit Root Tests 434 9.5.1 The Conditional Case 434 9.5.2 The Stationary Case 436 9.5.3 Power Properties 438 9.6 Unit Root Tests in the Dependent Case 444 9.6.1 The Conditional Case 444 9.6.2 The Stationary Case 446 9.7 The Relationship with Testing in the State Space Model 447 9.7.1 Case (I) 449 9.7.2 Case (II) 450 9.7.3 Case (III) 452 9.7.4 The Case of the Initial Value Known 454 10 Asymptotic Properties of Nonstationary Panel Unit Root Tests 459 10.1 Introduction 459 10.2 Panel Autoregressive Models 461 10.2.1 Tests Based on the OLSE 463 10.2.2 Tests Based on the GLSE 471 10.2.3 Some Other Tests 475 10.2.4 Limiting Power Envelopes 480 10.2.5 Graphical Comparison 485 10.3 Panel Moving Average Models 488 10.3.1 Conditional Case 490 10.3.2 Stationary Case 494 10.3.3 Power Envelope 499 10.3.4 Graphical Comparison 502 10.4 Panel Stationarity Tests 507 10.4.1 Limiting Local Powers 508 10.4.2 Power Envelope 512 10.4.3 Graphical Comparison 514 10.5 Concluding Remarks 515 11 Statistical Analysis of Cointegration 517 11.1 Introduction 517 11.2 Case of No Cointegration 519 11.3 Cointegration Distributions: The Independent Case 524 11.4 Cointegration Distributions: The Dependent Case 532 11.5 The Sampling Behavior of Cointegration Distributions 537 11.6 Testing for Cointegration 544 11.6.1 Tests for the Null of No Cointegration 544 11.6.2 Tests for the Null of Cointegration 547 11.7 Determination of the Cointegration Rank 552 11.8 Higher Order Cointegration 556 11.8.1 Cointegration in the I(d) Case 556 11.8.2 Seasonal Cointegration 559 Part II Analysis of Fractional Time Series 567 12 ARFIMA Models and the Fractional Brownian Motion 569 12.1 Nonstationary Fractional Time Series 569 12.1.1 Case of d = ½ 570 12.1.2 Case of d > ½ 572 12.2 Testing for the Fractional Integration Order 575 12.2.1 i.i.d. Case 575 12.2.2 Dependent Case 581 12.3 Estimation for the Fractional Integration Order 584 12.3.1 i.i.d. Case 584 12.3.2 Dependent Case 586 12.4 Stationary Long-Memory Processes 591 12.5 The Fractional Brownian Motion 597 12.6 FCLT for Long-Memory Processes 603 12.7 Fractional Cointegration 608 12.7.1 Spurious Regression in the Fractional Case 609 12.7.2 Cointegrating Regression in the Fractional Case 610 12.7.3 Testing for Fractional Cointegration 614 12.8 The Wavelet Method for ARFIMA Models and the fBm 614 12.8.1 Basic Theory of the Wavelet Transform 615 12.8.2 Some Advantages of the Wavelet Transform 618 12.8.3 Some Applications of the Wavelet Analysis 625 13 Statistical Inference Associated with the Fractional Brownian Motion 629 13.1 Introduction 629 13.2 A Simple Continuous-Time Model Driven by the fBm 632 13.3 Quadratic Functionals of the Brownian Motion 641 13.4 Derivation of the c.f. 645 13.4.1 Stochastic Process Approach via Girsanov’s Theorem 645 13.4.2 Fredholm Approach via the Fredholm Determinant 647 13.5 Martingale Approximation to the fBm 651 13.6 The Fractional Unit Root Distribution 659 13.6.1 The FD Associated with the Approximate Distribution 659 13.6.2 An Interesting Moment Property 664 13.7 The Unit Root Test Under the fBm Error 669 14 Maximum Likelihood Estimation for the Fractional Ornstein–Uhlenbeck Process 673 14.1 Introduction 673 14.2 Estimation of the Drift: Ergodic Case 677 14.2.1 Asymptotic Properties of the OLSEs 677 14.2.2 The MLE and MCE 679 14.3 Estimation of the Drift: Non-ergodic Case 687 14.3.1 Asymptotic Properties of the OLSE 687 14.3.2 The MLE 687 14.4 Estimation of the Drift: Boundary Case 692 14.4.1 Asymptotic Properties of the OLSEs 692 14.4.2 The MLE and MCE 693 14.5 Computation of Distributions and Moments of the MLE and MCE 695 14.6 The MLE-based Unit Root Test Under the fBm Error 703 14.7 Concluding Remarks 707 15 Solutions to Problems 709 References 865 Author Index 879 Subject Index 883

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Book SynopsisAn Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end. Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance is emphasized over statistical significance throTable of ContentsPreface xxiii 1 Introduction 1 1.1 Statistical Finance 2 1.2 Risk Management 3 1.3 Portfolio Management 5 1.4 Pricing of Securities 6 Part I Statistical Finance 11 2 Financial Instruments 13 2.1 Stocks 13 2.2 Fixed Income Instruments 19 2.3 Derivatives 23 2.4 Data Sets 27 3 Univariate Data Analysis 33 3.1 Univariate Statistics 34 3.2 Univariate Graphical Tools 42 3.3 Univariate ParametricModels 55 3.4 Tail Modeling 61 3.5 Asymptotic Distributions 83 3.6 Univariate Stylized Facts 91 4 Multivariate Data Analysis 95 4.1 Measures of Dependence 95 4.2 Multivariate Graphical Tools 103 4.3 Multivariate ParametricModels 107 4.4 Copulas 111 5 Time Series Analysis 121 5.1 Stationarity and Autocorrelation 122 5.2 Model Free Estimation 128 5.3 Univariate Time Series Models 135 5.4 Multivariate Time Series Models 157 5.5 Time Series Stylized Facts 160 6 Prediction 163 6.1 Methods of Prediction 164 6.2 Forecast Evaluation 170 6.3 Predictive Variables 175 6.4 Asset Return Prediction 182 Part II Risk Management 193 7 Volatility Prediction 195 7.1 Applications of Volatility Prediction 197 7.2 Performance Measures for Volatility Predictors 199 7.3 Conditional Heteroskedasticity Models 200 7.4 Moving Average Methods 205 7.5 State Space Predictors 211 8 Quantiles and Value-at-Risk 219 8.1 Definitions of Quantiles 220 8.2 Applications of Quantiles 223 8.3 Performance Measures for Quantile Estimators 227 8.4 Nonparametric Estimators of Quantiles 233 8.5 Volatility Based Quantile Estimation 240 8.6 Excess Distributions in Quantile Estimation 258 8.7 Extreme ValueTheory in Quantile Estimation 288 8.8 Expected Shortfall 292 Part III Portfolio Management 297 9 Some Basic Concepts of Portfolio Theory 299 9.1 Portfolios and Their Returns 300 9.2 Comparison of Return andWealth Distributions 312 9.3 Multiperiod Portfolio Selection 326 10 Performance Measurement 337 10.1 The Sharpe Ratio 338 10.2 Certainty Equivalent 346 10.3 Drawdown 347 10.4 Alpha and Conditional Alpha 348 10.5 Graphical Tools of Performance Measurement 356 11 Markowitz Portfolios 367 11.1 Variance Penalized Expected Return 369 11.2 Minimizing Variance under a Sufficient Expected Return 372 11.3 Markowitz Bullets 375 11.4 Further Topics in Markowitz Portfolio Selection 381 11.5 Examples of Markowitz Portfolio Selection 383 12 Dynamic Portfolio Selection 385 12.1 Prediction in Dynamic Portfolio Selection 387 12.2 Backtesting Trading Strategies 393 12.3 One Risky Asset 394 12.4 Two Risky Assets 405 Part IV Pricing of Securities 419 13 Principles of Asset Pricing 421 13.1 Introduction to Asset Pricing 422 13.2 Fundamental Theorems of Asset Pricing 430 13.3 Evaluation of Pricing and Hedging Methods 456 14 Pricing by Arbitrage 459 14.1 Futures and the Put–Call Parity 460 14.2 Pricing in Binary Models 466 14.3 Black–Scholes Pricing 485 14.4 Black–Scholes Hedging 505 14.5 Black–Scholes Hedging and Volatility Estimation 515 15 Pricing in IncompleteModels 521 15.1 Quadratic Hedging and Pricing 522 15.2 Utility Maximization 523 15.3 Absolutely Continuous Changes of Measures 530 15.4 GARCH Market Models 534 15.5 Nonparametric Pricing Using Historical Simulation 545 15.6 Estimation of the Risk-Neutral Density 551 15.7 Quantile Hedging 555 16 Quadratic and Local Quadratic Hedging 557 16.1 Quadratic Hedging 558 16.2 Local Quadratic Hedging 583 16.3 Implementations of Local Quadratic Hedging 595 17 Option Strategies 615 17.1 Option Strategies 616 17.2 Profitability of Option Strategies 625 18 Interest Rate Derivatives 649 18.1 Basic Concepts of Interest Rate Derivatives 650 18.2 Interest Rate Forwards 659 18.3 Interest Rate Options 666 18.4 Modeling Interest Rate Markets 669 References 673 Index 681

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