Time Series Analysis

by Cryer, Jonathan D.; Chan, Kung-Sik

• ISBN13: 9780387759586
• ISBN10: 0387759581
• Edition: 2nd
• Format: Hardcover
• Copyright: 2008-04-04
• Publisher: SPRINGER - VERLAG

Summary

Time Series Analysis With Applications in R, Second Edition, presents an accessible approach to understanding time series models and their applications. Although the emphasis is on time domain ARIMA models and their analysis, the new edition devotes two chapters to the frequency domain and three to time series regression models, models for heteroscedasticty, and threshold models. All of the ideas and methods are illustrated with both real and simulated data sets. A unique feature of this edition is its integration with the R computing environment. The tables and graphical displays are accompanied by the R commands used to produce them. An extensive R package, TSA, which contains many new or revised R functions and all of the data used in the book, accompanies the written text. Script files of R commands for each chapter are available for download. There is also an extensive appendix in the book that leads the reader through the use of R commands and the new R package to carry out the analyses.

Author Biography

Jonathan Cryer is Professor Emeritus, University of Iowa, in the Department of Statistics and Actuarial Science.

Table of Contents

Introduction	p. 1
Examples of Time Series	p. 1
A Model-Building Strategy	p. 8
Time Series Plots in History	p. 8
An Overview of the Book	p. 9
Exercises	p. 10
Fundamental Concepts	p. 11
Time Series and Stochastic Processes	p. 11
Means, Variances, and Covariances	p. 11
Stationarity	p. 16
Summary	p. 19
Exercises	p. 19
Expectation, Variance, Covariance, and Correlation	p. 24
Trends	p. 27
Deterministic Versus Stochastic Trends	p. 27
Estimation of a Constant Mean	p. 28
Regression Methods	p. 30
Reliability and Efficiency of Regression Estimates	p. 36
Interpreting Regression Output	p. 40
Residual Analysis	p. 42
Summary	p. 50
Exercises	p. 50
Models for Stationary Time Series	p. 55
General Linear Processes	p. 55
Moving Average Processes	p. 57
Autoregressive Processes	p. 66
The Mixed Autoregressive Moving Average Model	p. 77
Invertibility	p. 79
Summary	p. 80
Exercises	p. 81
The Stationarity Region for an AR(2) Process	p. 84
The Autocorrelation Function for ARMA(p,q)	p. 85
Models for Nonstationary Time Series	p. 87
Stationarity Through Differencing	p. 88
ARIMA Models	p. 92
Constant Terms in ARIMA Models	p. 97
Other Transformations	p. 98
Summary	p. 102
Exercises	p. 103
The Backshift Operator	p. 106
Model Specification	p. 109
Properties of the Sample Autocorrelation Function	p. 109
The Partial and Extended Autocorrelation Functions	p. 112
Specification of Some Simulated Time Series	p. 117
Nonstationarity	p. 125
Other Specification Methods	p. 130
Specification of Some Actual Time Series	p. 133
Summary	p. 141
Exercises	p. 141
Parameter Estimation	p. 149
The Method of Moments	p. 149
Least Squares Estimation	p. 154
Maximum Likelihood and Unconditional Least Squares	p. 158
Properties of the Estimates	p. 160
Illustrations of Parameter Estimation	p. 163
Bootstrapping ARIMA Models	p. 167
Summary	p. 170
Exercises	p. 170
Model Diagnostics	p. 175
Residual Analysis	p. 175
Overfitting and Parameter Redundancy	p. 185
Summary	p. 188
Exercises	p. 188
Forecasting	p. 191
Minimum Mean Square Error Forecasting	p. 191
Deterministic Trends	p. 191
ARIMA Forecasting	p. 193
Prediction Limits	p. 203
Forecasting Illustrations	p. 204
Updating ARIMA Forecasts	p. 207
Forecast Weights and Exponentially Weighted Moving Averages	p. 207
Forecasting Transformed Series	p. 209
Summary of Forecasting with Certain ARIMA Models	p. 211
Summary	p. 213
Exercises	p. 213
Conditional Expectation	p. 218
Minimum Mean Square Error Prediction	p. 218
The Truncated Linear Process	p. 221
State Space Models	p. 222
Seasonal Models	p. 227
Seasonal ARIMA Models	p. 228
Multiplicative Seasonal ARMA Models	p. 230
Nonstationary Seasonal ARIMA Models	p. 233
Model Specification, Fitting, and Checking	p. 234
Forecasting Seasonal Models	p. 241
Summary	p. 246
Exercises	p. 246
Time Series Regression Models	p. 249
Intervention Analysis	p. 249
Outliers	p. 257
Spurious Correlation	p. 260
Prewhitening and Stochastic Regression	p. 265
Summary	p. 273
Exercises	p. 274
Time Series Models of Heteroscedasticity	p. 277
Some Common Features of Financial Time Series	p. 278
The ARCH(1) Model	p. 285
GARCH Models	p. 289
Maximum Likelihood Estimation	p. 298
Model Diagnostics	p. 301
Conditions for the Nonnegativity of the Conditional Variances	p. 307
Some Extensions of the GARCH Model	p. 310
Another Example: The Daily USD/HKD Exchange Rates	p. 311
Summary	p. 315
Exercises	p. 316
Formulas for the Generalized Portmanteau Tests	p. 318
Introduction to Spectral Analysis	p. 319
Introduction	p. 319
The Periodogram	p. 322
The Spectral Representation and Spectral Distribution	p. 327
The Spectral Density	p. 330
Spectral Densities for ARMA Processes	p. 332
Sampling Properties of the Sample Spectral Density	p. 340
Summary	p. 346
Exercises	p. 346
Orthogonality of Cosine and Sine Sequences	p. 349
Estimating the Spectrum	p. 351
Smoothing the Spectral Density	p. 351
Bias and Variance	p. 354
Bandwidth	p. 355
Confidence Intervals for the Spectrum	p. 356
Leakage and Tapering	p. 358
Autoregressive Spectrum Estimation	p. 363
Examples with Simulated Data	p. 364
Examples with Actual Data	p. 370
Other Methods of Spectral Estimation	p. 376
Summary	p. 378
Exercises	p. 378
Tapering and the Dirichlet Kernel	p. 381
Threshold Models	p. 383
Graphically Exploring Nonlinearity	p. 384
Tests for Nonlinearity	p. 390
Polynomial Models Are Generally Explosive	p. 393
First-Order Threshold Autoregressive Models	p. 395
Threshold Models	p. 399
Testing for Threshold Nonlinearity	p. 400
Estimation of a TAR Model	p. 402
Model Diagnostics	p. 411
Prediction	p. 415
Summary	p. 420
Exercises	p. 420
The Generalized Portmanteau Test for TAR	p. 421
An Introduction to R	p. 423
Introduction	p. 423
Chapter 1 R Commands	p. 429
Chapter 2 R Commands	p. 433
Chapter 3 R Commands	p. 433
Chapter 4 R Commands	p. 438
Chapter 5 R Commands	p. 439
Chapter 6 R Commands	p. 441
Chapter 7 R Commands	p. 442
Chapter 8 R Commands	p. 446
Chapter 9 R Commands	p. 447
Chapter 10 R Commands	p. 450
Chapter 11 R Commands	p. 451
Chapter 12 R Commands	p. 457
Chapter 13 R Commands	p. 460
Chapter 14 R Commands	p. 461
Chapter 15 R Commands	p. 462
New or Enhanced Functions in the TSA Library	p. 468
Dataset Information	p. 471
Bibliography	p. 477
Index	p. 487
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