Time Series Analysis

Wilfredo Palma, PhD, is Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. Dr. Palma has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics. He is the author of Long-Memory Time Series: Theory and Methods, also published by Wiley.

"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

• Preface xiiiAcknowledgments xviiAcronyms xix1 Introduction 11.1 Time Series Data 21.2 Random Variables and Statistical Modeling 161.3 Discrete-Time Models 221.4 Serial Dependence 221.5 Nonstationarity 251.6 Whiteness Testing 321.7 Parametric and Nonparametric Modeling 361.8 Forecasting 381.9 Time Series Modeling 381.10 Bibliographic Notes 39Problems 392 Linear Processes 432.1 Definition 442.2 Stationarity 442.3 Invertibility 452.4 Causality 462.5 Representations of Linear Processes 462.6 Weak and Strong Dependence 492.7 ARMA Models 512.8 Autocovariance Function 562.9 ACF and Partial ACF Functions 572.10 ARFIMA Processes 642.11 Fractional Gaussian Noise 712.12 Bibliographic Notes 72Problems 723 State Space Models 893.1 Introduction 903.2 Linear Dynamical Systems 923.3 State space Modeling of Linear Processes 963.4 State Estimation 973.5 Exogenous Variables 1133.6 Bibliographic Notes 114Problems 1144 Spectral Analysis 1214.1 Time and Frequency Domains 1224.2 Linear Filters 1224.3 Spectral Density 1234.4 Periodogram 1254.5 Smoothed Periodogram 1284.6 Examples 1304.7 Wavelets 1364.8 Spectral Representation 1384.9 Time-Varying Spectrum 1404.10 Bibliographic Notes 145Problems 1455 Estimation Methods 1515.1 Model Building 1525.2 Parsimony 1525.3 Akaike and Schwartz Information Criteria 1535.4 Estimation of the Mean 1535.5 Estimation of Autocovariances 1545.6 Moment Estimation 1555.7 Maximum-Likelihood Estimation 1565.8 Whittle Estimation 1575.9 State Space Estimation 1605.10 Estimation of Long-Memory Processes 1615.11 Numerical Experiments 1785.12 Bayesian Estimation 1805.13 Statistical Inference 1845.14 Illustrations 1895.15 Bibliographic Notes 193Problems 1946 Nonlinear Time Series 2096.1 Introduction 2106.2 Testing for Linearity 2116.3 Heteroskedastic Data 2126.4 ARCH Models 2136.5 GARCH Models 2166.6 ARFIMA-GARCH Models 2186.7 ARCH(1) Models 2206.8 APARCH Models 2226.9 Stochastic Volatility 2226.10 Numerical Experiments 2236.11 Data Applications 2256.12 Value at Risk 2366.13 Autocorrelation of Squares 2416.14 Threshold autoregressive models 2476.15 Bibliographic Notes 252Problems 2537 Prediction 2677.1 Optimal Prediction 2687.2 One-Step Ahead Predictors 2687.3 Multistep Ahead Predictors 2757.4 Heteroskedastic Models 2767.5 Prediction Bands 2817.6 Data Application 2877.7 Bibliographic Notes 289Problems 2898 Nonstationary Processes 2958.1 Introduction 2968.2 Unit Root Testing 2978.3 ARIMA Processes 2988.4 Locally Stationary Processes 3018.5 Structural Breaks 3268.6 Bibliographic Notes 331Problems 3329 Seasonality 3379.1 SARIMA Models 3389.2 SARFIMA Models 3519.3 GARMA Models 3539.4 Calculation of the Asymptotic Variance 3559.5 Autocovariance Function 3559.6 Monte Carlo Studies 3599.7 Illustration 3629.8 Bibliographic Notes 364Problems 36510 Time Series Regression 36910.1 Motivation 37010.2 Definitions 37310.3 Properties of the LSE 37510.4 Properties of the BLUE 37610.5 Estimation of the Mean 37910.6 Polynomial Trend 38210.7 Harmonic Regression 38610.8 Illustration: Air Pollution Data 38810.9 Bibliographic Notes 392Problems 39211 Missing Values and Outliers 39911.1 Introduction 40011.2 Likelihood Function with Missing Values 40111.3 Effects of Missing Values on ML Estimates 40511.4 Effects of Missing Values on Prediction 40711.5 Interpolation of Missing Data 41011.6 Spectral Estimation with Missing Values 41811.7 Outliers and Intervention Analysis 42111.8 Bibliographic Notes 434Problems 43512 Non-Gaussian Time Series 44112.1 Data Driven Models 44212.2 Parameter Driven Models 45212.3 Estimation 45312.4 Data Illustrations 46612.5 Zero-Inflated Models 47712.6 Bibliographic Notes 483Problems 483Appendix A: Complements 487A.1 Projection Theorem 488A.2 Wold Decomposition 490A.3 Bibliographic Notes 497Appendix B: Solutions to Selected Problems 499Appendix C: Data and Codes 557References 559Topic Index 573Author Index 577