{"product_id":"longmemory-time-series-theory-and-methods-662-wiley-series-in-probability-and-statistics-9780470114025","title":"LongMemory Time Series Theory and Methods 662","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDuring the last decades long-memory processes have evolved as a vital and important part of time series analysis. This book attempts to give an overview of the theory and methods developed to deal with long-range dependent data as well as describe some applications of these methodologies to real-life time series.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"...Palma presents a textbook for a graduate course summarizing the theory and methods developed to deal with long-range-dependent data, and describing some applications to real-life time series.\" (\u003ci\u003eSciTech Book Reviews\u003c\/i\u003e, June 2007)  \u003cp\u003e\"...textbook for a graduate course summarizing the theory and methods developed to deal with long-range-dependent data, and describing some applications to real-life time series.... Problems and bibliographic notes are provided at the end of each chapter.\" (\u003ci\u003eSciTech Book News\u003c\/i\u003e, June 2007)\u003c\/p\u003e \u003cp\u003e\"I believe that this text provides an important contribution to the long-memory time series literature. I feel that it largely achieves its aims and could be useful for those instructors wishing to teach a semester-long special topics course.... I strongly recommend this book to anyone interested in long-memory time series. Both researchers and beginners alike will find this text extremely useful.\" (\u003ci\u003eJournal of the American Statisticial\u003c\/i\u003e \u003ci\u003eAssociatio\u003c\/i\u003en\u003ci\u003e,\u003c\/i\u003e Dec 2008)\u003c\/p\u003e \u003cp\u003e\"Very well-organized catalogue of long-memory time series analysis.\" (\u003ci\u003eMathematical Reviews\u003c\/i\u003e, 2008)\u003c\/p\u003e \u003cp\u003e\"Judging by its contents and scope [the aim of this book] has been largely achieved.... The list of references is selective but quite comprehensive. Each chapter concludes with a 'Problems' section which should be helpful to instructors wishing to use this book as standalone basis for a course in its subject area...\" (\u003ci\u003eInternational Statistical Review\u003c\/i\u003e, 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcronyms xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Stationary Precedes 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Fundamental concepts 2\u003c\/p\u003e \u003cp\u003e1.1.1 Stationarity 4\u003c\/p\u003e \u003cp\u003e1.1.2 Singularity and Regularity 5\u003c\/p\u003e \u003cp\u003e1.1.3 Wold Decomposition Theorem 5\u003c\/p\u003e \u003cp\u003e1.1.4 Causality 7\u003c\/p\u003e \u003cp\u003e1.1.5 Invertibility 7\u003c\/p\u003e \u003cp\u003e1.1.6 Best Linear Predictor 8\u003c\/p\u003e \u003cp\u003e1.1.7 Szego-Kolmogorov Formula 8\u003c\/p\u003e \u003cp\u003e1.1.8 Ergodicity 9\u003c\/p\u003e \u003cp\u003e1.1.9 Martingales 11\u003c\/p\u003e \u003cp\u003e1.1.10 Cumulants 12\u003c\/p\u003e \u003cp\u003e1.1.11 Fractional Brownian Motion 12\u003c\/p\u003e \u003cp\u003e1.1.12 Wavelets 14\u003c\/p\u003e \u003cp\u003e1.2 Bibliographic Notes 15\u003c\/p\u003e \u003cp\u003eProblems 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 State Space Systems 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 22\u003c\/p\u003e \u003cp\u003e2.1.1 Stability 22\u003c\/p\u003e \u003cp\u003e2.1.2 Hankel Operator 22\u003c\/p\u003e \u003cp\u003e2.1.3 Observability 23\u003c\/p\u003e \u003cp\u003e2.1.4 Controllability 23\u003c\/p\u003e \u003cp\u003e2.1.5 Minimality 24\u003c\/p\u003e \u003cp\u003e2.2 Representations of Linear Processes 24\u003c\/p\u003e \u003cp\u003e2.2.1 State Space Form to Wold Decomposition 24\u003c\/p\u003e \u003cp\u003e2.2.2 Wold Decomposition to State Form 25\u003c\/p\u003e \u003cp\u003e2.2.3 Hankel Operator to State Space Form 25\u003c\/p\u003e \u003cp\u003e2.3 Estimation of the State 26\u003c\/p\u003e \u003cp\u003e2.3.1 State Predictor 27\u003c\/p\u003e \u003cp\u003e2.3.2 State Filter 27\u003c\/p\u003e \u003cp\u003e2.3.3 State Smoother 27\u003c\/p\u003e \u003cp\u003e2.3.4 Missing Observation 28\u003c\/p\u003e \u003cp\u003e2.3.5 Steady State System 28\u003c\/p\u003e \u003cp\u003e2.3.6 Prediction of Future Observations 30\u003c\/p\u003e \u003cp\u003e2.4 Extensions 32\u003c\/p\u003e \u003cp\u003e2.5 Bibliographic Notes 32\u003c\/p\u003e \u003cp\u003eProblems 33\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Long-Memory\/Processes 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Defining Long Memory 40\u003c\/p\u003e \u003cp\u003e3.1.1 Alternative Definitions 41\u003c\/p\u003e \u003cp\u003e3.1.2 Extensions 43\u003c\/p\u003e \u003cp\u003e3.2 ARFIMA Processes 43\u003c\/p\u003e \u003cp\u003e3.2.1 Stationarity, Causality, and Invertibility 44\u003c\/p\u003e \u003cp\u003e3.2.2 Infinite AR and MA Expansions 46\u003c\/p\u003e \u003cp\u003e3.2.3 Spectral Density 47\u003c\/p\u003e \u003cp\u003e3.2.4 Autocovariance Function 47\u003c\/p\u003e \u003cp\u003e3.2.5 Sample Mean 48\u003c\/p\u003e \u003cp\u003e3.2.6 Partial Autocorrelations 49\u003c\/p\u003e \u003cp\u003e3.2.7 Illustrations 49\u003c\/p\u003e \u003cp\u003e3.2.8 Approximation of Long-Memory Processes 55\u003c\/p\u003e \u003cp\u003e3.3 Fractional Gaussian Noise 56\u003c\/p\u003e \u003cp\u003e3.3.1 Sample Mean 56\u003c\/p\u003e \u003cp\u003e3.4 Technical Lemmas 57\u003c\/p\u003e \u003cp\u003e3.5 Bibliographic Notes 58\u003c\/p\u003e \u003cp\u003eProblems 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Estimation Methods 65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Maximum-Likelihood Estimation 66\u003c\/p\u003e \u003cp\u003e4.1.1 Cholesky Decomposition Method 66\u003c\/p\u003e \u003cp\u003e4.1.2 Durbin-Levinson Algorithm 66\u003c\/p\u003e \u003cp\u003e4.1.3 Computation of Autocovariances 67\u003c\/p\u003e \u003cp\u003e4.1.4 State Space Approach 69\u003c\/p\u003e \u003cp\u003e4.2 Autoregressive Approximations 71\u003c\/p\u003e \u003cp\u003e4.2.1 Haslett-Raftery Method72\u003c\/p\u003e \u003cp\u003e4.2.2 Beran Approach 73\u003c\/p\u003e \u003cp\u003e4.2.3 A State Space Method 74\u003c\/p\u003e \u003cp\u003e4.3 Moving-Average Approximation 75\u003c\/p\u003e \u003cp\u003e4.4 Whittle Estimation 78\u003c\/p\u003e \u003cp\u003e4.4.1 Other versions 80\u003c\/p\u003e \u003cp\u003e4.4.2 Non-Gaussian Data 80\u003c\/p\u003e \u003cp\u003e4.4.3 Semiparametric Methods 81\u003c\/p\u003e \u003cp\u003e4.5 Other Methods 81\u003c\/p\u003e \u003cp\u003e4.5.1 A Regression Method 82\u003c\/p\u003e \u003cp\u003e4.5.2 Rescale Range Method 83\u003c\/p\u003e \u003cp\u003e4.5.3 Variance Plots 85\u003c\/p\u003e \u003cp\u003e4.5.4 Detrended Fluctuation Analysis 87\u003c\/p\u003e \u003cp\u003e4.5.5 A Wavelet-Based Method 91\u003c\/p\u003e \u003cp\u003e4.6 Numerical Experiments 92\u003c\/p\u003e \u003cp\u003e4.7 Bibliographic Notes 93\u003c\/p\u003e \u003cp\u003eProblems 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Asymptotic Theory 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Notation and Definitions 98\u003c\/p\u003e \u003cp\u003e5.2 Theorems 99\u003c\/p\u003e \u003cp\u003e5.2.1 Consistency 99\u003c\/p\u003e \u003cp\u003e5.2.2 Central Limit Theorem 101\u003c\/p\u003e \u003cp\u003e5.2.3 Efficiency 104\u003c\/p\u003e \u003cp\u003e5.3 Examples 104\u003c\/p\u003e \u003cp\u003e5.4 Illustration 108\u003c\/p\u003e \u003cp\u003e5.5 Technical Lemmas 109\u003c\/p\u003e \u003cp\u003e5.6 Bibliographic Notes 109\u003c\/p\u003e \u003cp\u003eProblems 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Heteroskedastic Models 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 116\u003c\/p\u003e \u003cp\u003e6.2 ARFIMA-GARCH Model 117\u003c\/p\u003e \u003cp\u003e6.2.1 Estimation 119\u003c\/p\u003e \u003cp\u003e6.3 Other Models 119\u003c\/p\u003e \u003cp\u003e6.3.1 Estimation 121\u003c\/p\u003e \u003cp\u003e6.4 Stochastic Volatility 121\u003c\/p\u003e \u003cp\u003e6.4.1 Estimation 122\u003c\/p\u003e \u003cp\u003e6.5 Numerical Experiments 122\u003c\/p\u003e \u003cp\u003e6.6 Application 123\u003c\/p\u003e \u003cp\u003e6.6.1 Model without Leverage 123\u003c\/p\u003e \u003cp\u003e6.6.2 Model with Leverage 124\u003c\/p\u003e \u003cp\u003e6.6.3 Model Comparison 124\u003c\/p\u003e \u003cp\u003e6.7 Bibliographic Notes 125\u003c\/p\u003e \u003cp\u003eProblems 126\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Transformations 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Transformation of Gaussian Processes 132\u003c\/p\u003e \u003cp\u003e7.2 Autocorrelation of Squares 134\u003c\/p\u003e \u003cp\u003e7.3 Asymptotic behavior 136\u003c\/p\u003e \u003cp\u003e7.4 Illustrations 138\u003c\/p\u003e \u003cp\u003e7.5 Bibliographic Notes 142\u003c\/p\u003e \u003cp\u003eProblems 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Bayesian Methods 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Bayesian Modeling 148\u003c\/p\u003e \u003cp\u003e8.2 Markov Chain Monte Carlo Methods 149\u003c\/p\u003e \u003cp\u003e8.2.1 Metropolis-Hastings Algorithm 149\u003c\/p\u003e \u003cp\u003e8.2.2 Gibbs Sampler 150\u003c\/p\u003e \u003cp\u003e8.2.3 Overdispersed Distributions 152\u003c\/p\u003e \u003cp\u003e8.3 Monitoring Convergence 153\u003c\/p\u003e \u003cp\u003e8.4 A Simulated Example 155\u003c\/p\u003e \u003cp\u003e8.5 Data Application 158\u003c\/p\u003e \u003cp\u003e8.6 Bibliographic Notes 162\u003c\/p\u003e \u003cp\u003eProblems 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Prediction 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 One-Step Ahead Predictors 168\u003c\/p\u003e \u003cp\u003e9.1.1 Infinite Past 168\u003c\/p\u003e \u003cp\u003e9.1.2 Finite Past 168\u003c\/p\u003e \u003cp\u003e9.1.3 An Approximate Predictor 172\u003c\/p\u003e \u003cp\u003e9.2 Multistep Ahead Predictors 173\u003c\/p\u003e \u003cp\u003e9.2.1 Infinite Past 173\u003c\/p\u003e \u003cp\u003e9.2.2 Finite Past 174\u003c\/p\u003e \u003cp\u003e9.3 Heteroskedastic Models 175\u003c\/p\u003e \u003cp\u003e9.3.1 Prediction of Volatility 176\u003c\/p\u003e \u003cp\u003e9.4 Illustration 178\u003c\/p\u003e \u003cp\u003e9.5 Rational Approximations 180\u003c\/p\u003e \u003cp\u003e9.5.1 Illustration 182\u003c\/p\u003e \u003cp\u003e9.6 Bibliographic Notes Problems 184\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Regression\u003c\/b\u003e \u003cb\u003e187 \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Linear Regression Model 188\u003c\/p\u003e \u003cp\u003e10.1.1 Grenander conditions 188\u003c\/p\u003e \u003cp\u003e10.2 Properties of the LSE 191\u003c\/p\u003e \u003cp\u003e10.2.1 Consistency 192\u003c\/p\u003e \u003cp\u003e10.2.2 Asymptotic Variance 193\u003c\/p\u003e \u003cp\u003e10.2.3 Asymptotic Normality 193\u003c\/p\u003e \u003cp\u003e10.3 Properties of the BLUE 194\u003c\/p\u003e \u003cp\u003e10.3.1 Efficiency of the LSE Relative to the BLUE 195\u003c\/p\u003e \u003cp\u003e10.4 Estimation of the Mean 198\u003c\/p\u003e \u003cp\u003e10.4.1 Consistency 198\u003c\/p\u003e \u003cp\u003e10.4.2 Asymptotic Variance 199\u003c\/p\u003e \u003cp\u003e10.4.3 Normality 200\u003c\/p\u003e \u003cp\u003e10.4.4 Relative Efficiency 200\u003c\/p\u003e \u003cp\u003e10.5 Polynomial Trend 202\u003c\/p\u003e \u003cp\u003e10.5.1 Consistency 203\u003c\/p\u003e \u003cp\u003e10.5.2 Asymptotic Variance 203\u003c\/p\u003e \u003cp\u003e10.5.3 Normality 204\u003c\/p\u003e \u003cp\u003e10.5.4 Relative Efficiency 204\u003c\/p\u003e \u003cp\u003e10.6 Harmonic Regression 205\u003c\/p\u003e \u003cp\u003e10.6.1 Consistency 205\u003c\/p\u003e \u003cp\u003e10.6.2 Asymptotic Variance 205\u003c\/p\u003e \u003cp\u003e10.6.3 Normality 205\u003c\/p\u003e \u003cp\u003e10.6.4 Efficiency 206\u003c\/p\u003e \u003cp\u003e10.7 Illustration: Air Pollution Data 207\u003c\/p\u003e \u003cp\u003e10.8 Bibliographic Notes 210\u003c\/p\u003e \u003cp\u003eProblems 211\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Missing Data 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Motivation 216\u003c\/p\u003e \u003cp\u003e11.2 Likelihood Function with Incomplete Data 217\u003c\/p\u003e \u003cp\u003e11.2.1 Integration 217\u003c\/p\u003e \u003cp\u003e11.2.2 Maximization 218\u003c\/p\u003e \u003cp\u003e11.2.3 Calculation of the Likelihood Function 219\u003c\/p\u003e \u003cp\u003e11.2.4 Kalman Filter with Missing Observations 219\u003c\/p\u003e \u003cp\u003e11.3 Effects of Missing Values on ML Estimates 221\u003c\/p\u003e \u003cp\u003e11.3.1 Monte Carlo Experiments 222\u003c\/p\u003e \u003cp\u003e11.4 Effects of Missing Values on Prediction 223\u003c\/p\u003e \u003cp\u003e11.5 Illustrations 227\u003c\/p\u003e \u003cp\u003e11.6 Interpolation of Missing Data 229\u003c\/p\u003e \u003cp\u003e11.6.1 Bayesian Imputation 234\u003c\/p\u003e \u003cp\u003e11.6.2 A Simulated Example 235\u003c\/p\u003e \u003cp\u003e11.7 Bibliographic Notes 239\u003c\/p\u003e \u003cp\u003eProblems 239\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Seasonality 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 A Long-Memory Seasonal Model 246\u003c\/p\u003e \u003cp\u003e12.2 Calculation of the Asymptotic Variance 250\u003c\/p\u003e \u003cp\u003e12.3 Autocovariance Function 252\u003c\/p\u003e \u003cp\u003e12.4 Monte Carlo Studies 254\u003c\/p\u003e \u003cp\u003e12.5 Illustration 258\u003c\/p\u003e \u003cp\u003e12.6 Bibliographic Notes 260\u003c\/p\u003e \u003cp\u003eProblems 261\u003c\/p\u003e \u003cp\u003eReferences 265\u003c\/p\u003e \u003cp\u003eTopic Index 279\u003c\/p\u003e \u003cp\u003eAuthor Index 283\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402287948119,"sku":"9780470114025","price":116.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470114025.jpg?v=1730479957","url":"https:\/\/bookcurl.com\/products\/longmemory-time-series-theory-and-methods-662-wiley-series-in-probability-and-statistics-9780470114025","provider":"Book 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