Time Series Analysis: With Applications in R

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2008-04-04
  • Publisher: Springer Verlag

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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

Introductionp. 1
Examples of Time Seriesp. 1
A Model-Building Strategyp. 8
Time Series Plots in Historyp. 8
An Overview of the Bookp. 9
Exercisesp. 10
Fundamental Conceptsp. 11
Time Series and Stochastic Processesp. 11
Means, Variances, and Covariancesp. 11
Stationarityp. 16
Summaryp. 19
Exercisesp. 19
Expectation, Variance, Covariance, and Correlationp. 24
Trendsp. 27
Deterministic Versus Stochastic Trendsp. 27
Estimation of a Constant Meanp. 28
Regression Methodsp. 30
Reliability and Efficiency of Regression Estimatesp. 36
Interpreting Regression Outputp. 40
Residual Analysisp. 42
Summaryp. 50
Exercisesp. 50
Models for Stationary Time Seriesp. 55
General Linear Processesp. 55
Moving Average Processesp. 57
Autoregressive Processesp. 66
The Mixed Autoregressive Moving Average Modelp. 77
Invertibilityp. 79
Summaryp. 80
Exercisesp. 81
The Stationarity Region for an AR(2) Processp. 84
The Autocorrelation Function for ARMA(p,q)p. 85
Models for Nonstationary Time Seriesp. 87
Stationarity Through Differencingp. 88
ARIMA Modelsp. 92
Constant Terms in ARIMA Modelsp. 97
Other Transformationsp. 98
Summaryp. 102
Exercisesp. 103
The Backshift Operatorp. 106
Model Specificationp. 109
Properties of the Sample Autocorrelation Functionp. 109
The Partial and Extended Autocorrelation Functionsp. 112
Specification of Some Simulated Time Seriesp. 117
Nonstationarityp. 125
Other Specification Methodsp. 130
Specification of Some Actual Time Seriesp. 133
Summaryp. 141
Exercisesp. 141
Parameter Estimationp. 149
The Method of Momentsp. 149
Least Squares Estimationp. 154
Maximum Likelihood and Unconditional Least Squaresp. 158
Properties of the Estimatesp. 160
Illustrations of Parameter Estimationp. 163
Bootstrapping ARIMA Modelsp. 167
Summaryp. 170
Exercisesp. 170
Model Diagnosticsp. 175
Residual Analysisp. 175
Overfitting and Parameter Redundancyp. 185
Summaryp. 188
Exercisesp. 188
Forecastingp. 191
Minimum Mean Square Error Forecastingp. 191
Deterministic Trendsp. 191
ARIMA Forecastingp. 193
Prediction Limitsp. 203
Forecasting Illustrationsp. 204
Updating ARIMA Forecastsp. 207
Forecast Weights and Exponentially Weighted Moving Averagesp. 207
Forecasting Transformed Seriesp. 209
Summary of Forecasting with Certain ARIMA Modelsp. 211
Summaryp. 213
Exercisesp. 213
Conditional Expectationp. 218
Minimum Mean Square Error Predictionp. 218
The Truncated Linear Processp. 221
State Space Modelsp. 222
Seasonal Modelsp. 227
Seasonal ARIMA Modelsp. 228
Multiplicative Seasonal ARMA Modelsp. 230
Nonstationary Seasonal ARIMA Modelsp. 233
Model Specification, Fitting, and Checkingp. 234
Forecasting Seasonal Modelsp. 241
Summaryp. 246
Exercisesp. 246
Time Series Regression Modelsp. 249
Intervention Analysisp. 249
Outliersp. 257
Spurious Correlationp. 260
Prewhitening and Stochastic Regressionp. 265
Summaryp. 273
Exercisesp. 274
Time Series Models of Heteroscedasticityp. 277
Some Common Features of Financial Time Seriesp. 278
The ARCH(1) Modelp. 285
GARCH Modelsp. 289
Maximum Likelihood Estimationp. 298
Model Diagnosticsp. 301
Conditions for the Nonnegativity of the Conditional Variancesp. 307
Some Extensions of the GARCH Modelp. 310
Another Example: The Daily USD/HKD Exchange Ratesp. 311
Summaryp. 315
Exercisesp. 316
Formulas for the Generalized Portmanteau Testsp. 318
Introduction to Spectral Analysisp. 319
Introductionp. 319
The Periodogramp. 322
The Spectral Representation and Spectral Distributionp. 327
The Spectral Densityp. 330
Spectral Densities for ARMA Processesp. 332
Sampling Properties of the Sample Spectral Densityp. 340
Summaryp. 346
Exercisesp. 346
Orthogonality of Cosine and Sine Sequencesp. 349
Estimating the Spectrump. 351
Smoothing the Spectral Densityp. 351
Bias and Variancep. 354
Bandwidthp. 355
Confidence Intervals for the Spectrump. 356
Leakage and Taperingp. 358
Autoregressive Spectrum Estimationp. 363
Examples with Simulated Datap. 364
Examples with Actual Datap. 370
Other Methods of Spectral Estimationp. 376
Summaryp. 378
Exercisesp. 378
Tapering and the Dirichlet Kernelp. 381
Threshold Modelsp. 383
Graphically Exploring Nonlinearityp. 384
Tests for Nonlinearityp. 390
Polynomial Models Are Generally Explosivep. 393
First-Order Threshold Autoregressive Modelsp. 395
Threshold Modelsp. 399
Testing for Threshold Nonlinearityp. 400
Estimation of a TAR Modelp. 402
Model Diagnosticsp. 411
Predictionp. 415
Summaryp. 420
Exercisesp. 420
The Generalized Portmanteau Test for TARp. 421
An Introduction to Rp. 423
Introductionp. 423
Chapter 1 R Commandsp. 429
Chapter 2 R Commandsp. 433
Chapter 3 R Commandsp. 433
Chapter 4 R Commandsp. 438
Chapter 5 R Commandsp. 439
Chapter 6 R Commandsp. 441
Chapter 7 R Commandsp. 442
Chapter 8 R Commandsp. 446
Chapter 9 R Commandsp. 447
Chapter 10 R Commandsp. 450
Chapter 11 R Commandsp. 451
Chapter 12 R Commandsp. 457
Chapter 13 R Commandsp. 460
Chapter 14 R Commandsp. 461
Chapter 15 R Commandsp. 462
New or Enhanced Functions in the TSA Libraryp. 468
Dataset Informationp. 471
Bibliographyp. 477
Indexp. 487
Table of Contents provided by Ingram. All Rights Reserved.

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