Description
Book SynopsisA modern and accessible guide to the analysis of introductory time series data Featuring an organized and self-contained guide, Time Series Analysis provides a broad introduction to the most fundamental methodologies and techniques of time series analysis.
Trade Review"This book offers a comprehensive overview of time series analysis...The focus throughout is on methodologies and techniques selected to help the reader develop a working knowledge of practical applications of time series methods... The author manages to incorporate a huge number of topics and his book verges on the encyclopedic...This is a book that would likely be of more use to a serious practitioner of time series analysis than anyone coming fresh to the subject." (Mathematical Association of America 29/03/2017)
“The book has many merits, covering carefully standard basic vocabulary of recently developing time series analysis and presenting lots of illustrative examples of applications that are well organized for the reader who intends to use R libraries for numerical computation” Yuzo Hosoya, MathSciNet, Aug 2017
Table of ContentsPreface xiii
Acknowledgments xvii
Acronyms xix
1 Introduction 1
1.1 Time Series Data 2
1.2 Random Variables and Statistical Modeling 16
1.3 Discrete-Time Models 22
1.4 Serial Dependence 22
1.5 Nonstationarity 25
1.6 Whiteness Testing 32
1.7 Parametric and Nonparametric Modeling 36
1.8 Forecasting 38
1.9 Time Series Modeling 38
1.10 Bibliographic Notes 39
Problems 39
2 Linear Processes 43
2.1 Definition 44
2.2 Stationarity 44
2.3 Invertibility 45
2.4 Causality 46
2.5 Representations of Linear Processes 46
2.6 Weak and Strong Dependence 49
2.7 ARMA Models 51
2.8 Autocovariance Function 56
2.9 ACF and Partial ACF Functions 57
2.10 ARFIMA Processes 64
2.11 Fractional Gaussian Noise 71
2.12 Bibliographic Notes 72
Problems 72
3 State Space Models 89
3.1 Introduction 90
3.2 Linear Dynamical Systems 92
3.3 State space Modeling of Linear Processes 96
3.4 State Estimation 97
3.5 Exogenous Variables 113
3.6 Bibliographic Notes 114
Problems 114
4 Spectral Analysis 121
4.1 Time and Frequency Domains 122
4.2 Linear Filters 122
4.3 Spectral Density 123
4.4 Periodogram 125
4.5 Smoothed Periodogram 128
4.6 Examples 130
4.7 Wavelets 136
4.8 Spectral Representation 138
4.9 Time-Varying Spectrum 140
4.10 Bibliographic Notes 145
Problems 145
5 Estimation Methods 151
5.1 Model Building 152
5.2 Parsimony 152
5.3 Akaike and Schwartz Information Criteria 153
5.4 Estimation of the Mean 153
5.5 Estimation of Autocovariances 154
5.6 Moment Estimation 155
5.7 Maximum-Likelihood Estimation 156
5.8 Whittle Estimation 157
5.9 State Space Estimation 160
5.10 Estimation of Long-Memory Processes 161
5.11 Numerical Experiments 178
5.12 Bayesian Estimation 180
5.13 Statistical Inference 184
5.14 Illustrations 189
5.15 Bibliographic Notes 193
Problems 194
6 Nonlinear Time Series 209
6.1 Introduction 210
6.2 Testing for Linearity 211
6.3 Heteroskedastic Data 212
6.4 ARCH Models 213
6.5 GARCH Models 216
6.6 ARFIMA-GARCH Models 218
6.7 ARCH(1) Models 220
6.8 APARCH Models 222
6.9 Stochastic Volatility 222
6.10 Numerical Experiments 223
6.11 Data Applications 225
6.12 Value at Risk 236
6.13 Autocorrelation of Squares 241
6.14 Threshold autoregressive models 247
6.15 Bibliographic Notes 252
Problems 253
7 Prediction 267
7.1 Optimal Prediction 268
7.2 One-Step Ahead Predictors 268
7.3 Multistep Ahead Predictors 275
7.4 Heteroskedastic Models 276
7.5 Prediction Bands 281
7.6 Data Application 287
7.7 Bibliographic Notes 289
Problems 289
8 Nonstationary Processes 295
8.1 Introduction 296
8.2 Unit Root Testing 297
8.3 ARIMA Processes 298
8.4 Locally Stationary Processes 301
8.5 Structural Breaks 326
8.6 Bibliographic Notes 331
Problems 332
9 Seasonality 337
9.1 SARIMA Models 338
9.2 SARFIMA Models 351
9.3 GARMA Models 353
9.4 Calculation of the Asymptotic Variance 355
9.5 Autocovariance Function 355
9.6 Monte Carlo Studies 359
9.7 Illustration 362
9.8 Bibliographic Notes 364
Problems 365
10 Time Series Regression 369
10.1 Motivation 370
10.2 Definitions 373
10.3 Properties of the LSE 375
10.4 Properties of the BLUE 376
10.5 Estimation of the Mean 379
10.6 Polynomial Trend 382
10.7 Harmonic Regression 386
10.8 Illustration: Air Pollution Data 388
10.9 Bibliographic Notes 392
Problems 392
11 Missing Values and Outliers 399
11.1 Introduction 400
11.2 Likelihood Function with Missing Values 401
11.3 Effects of Missing Values on ML Estimates 405
11.4 Effects of Missing Values on Prediction 407
11.5 Interpolation of Missing Data 410
11.6 Spectral Estimation with Missing Values 418
11.7 Outliers and Intervention Analysis 421
11.8 Bibliographic Notes 434
Problems 435
12 Non-Gaussian Time Series 441
12.1 Data Driven Models 442
12.2 Parameter Driven Models 452
12.3 Estimation 453
12.4 Data Illustrations 466
12.5 Zero-Inflated Models 477
12.6 Bibliographic Notes 483
Problems 483
Appendix A: Complements 487
A.1 Projection Theorem 488
A.2 Wold Decomposition 490
A.3 Bibliographic Notes 497
Appendix B: Solutions to Selected Problems 499
Appendix C: Data and Codes 557
References 559
Topic Index 573
Author Index 577
