Table of contents for Time series analysis and its applications : with R examples / Robert H. Shumway, David S. Stoffer.


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1 Characteristics of Time Series                                   1
1.1  Introduction  ..................         ..........    .   1
1.2  The Nature of Time Series Data . . . . . . . . . . . . . . . ..  4
1.3  Time Series Statistical Models . . . . . . . . . . . . . . . ...  11
1.4  Measures of Dependence: Autocorrelation
and Cross-Correlation . . . . . . . . . . . .  . . . .  . . 18
1.5  Stationary Time Series ..... . . . . . . . .  .  . . . .  .  23
1.6  Estimation of Correlation . . . . . . . . . . . . . . . ... .  29
1.7  Vector-Valued and Multidimensional Series . . . . . . . ....  34
Problems ........ .         .....................         .    40
2  Time Series Regression and Exploratory Data Analysis          48
2.1  Introduction  .............   ......    ....  .........   48
2.2  Classical Regression in the Time Series Context . . . . . . ...  49
2.3  Exploratory Data Analysis . . . . . . . .  . .  .   . . . ..57
2.4  Smoothing in the Time Series Context . . . . . . . . . . . ...  71
Problems ........       ......... ....... ...........          79
3  ARIMA Models                                                   84
3.1  Introduction  ...............      ..  .   . ....... ..   84
3.2  Autoregressive Moving Average Models . . . . . . . . . ....  85
3.3  Difference Equations . . . . . . . . . . . . . . .... ......  98
3.4  Autocorrelation and Partial Autocorrelation Functions . . . . . 103
3.5  Forecasting .................. .......... 110
3.6  Estim ation  ....................          .....    ....  122
3.7 Integrated Models for Nonstationary Data . . . . . . . . . ...  140
3.8  Building ARIMA Models ... . . . . . . .   . . . . . .....  143
3.9  Multiplicative Seasonal ARIMA Models . . . . . . . . . . ...  154
Problems ........ ..        ... . ........     .......     .  165
4  Spectral Analysis and Filtering                              174
4.1  Introduction  ............    .       .    . .........   174
4.2  Cyclical Behavior and Periodicity . . . . . . . . . . . . . ...  176
4.3  The Spectral Density  ........................           181
4.4 Periodogram and Discrete Fourier Transform  . . . . . . . ...  187
4.5 Nonparametric Spectral Estimation . . . . . . . . . . . . .... 197
4.6 Multiple Series and Cross-Spectra. .. . . . . . .  . . . .....  215
4.7  Linear Filters  .  ...........................        220
4.8 Parametric Spectral Estimation . . . . . . . .  .  .  .  .  .  .....  228
4.9 Dynamic Fourier Analysis and Wavelets . . . . . . . . . . ...  232
4.10 Lagged Regression Models  . ................... ..245
4.11 Signal Extraction and Optimum Filtering . . . . . . . . . .. .  251
4.12 Spectral Analysis of Multidimensional Series . . . . . . . . ...  256
Problems  .... . .................. .          .  .  .  .  .  .  .... 258
5 Additional Time Domain Topics                              271
5.1  Introduction  ...........   ....     . ............   271
5.2 Long Memory ARMA and Fractional Differencing . ...... ..271
5.3  GARCH  Models  . . ........................ ..280
5.4  Threshold  Models . ..................       .  ..... . .. 289
5.5 Regression with Autocorrelated Errors . . . . . . . . . .....  293
5.6 Lagged Regression: Transfer Function Modeling . . . . . . ...  295
5.7 Multivariate ARMAX Models ... . . . . . .  . . . . .....  302
Problems  . . ................. . . . .      .   .  .   . . .. 320
6 State-Space Models                                         324
6.1 Introduction . ......... ................         . ... 324
6.2 Filtering, Smoothing, and Forecasting . . . . . . . . . . .... 330
6.3 Maximum Likelihood Estimation ..... . . . . . .  . . . .....  339
6.4 Missing Data Modifications . . . . . . . . .  .  .  .   .  . ..348
6.5 Structural Models: Signal Extraction and Forecasting . . . . . 352
6.6 ARMAX Models in State-Space Form  . . . . . . . . . .....  355
6.7 Bootstrapping State-Space Models . . . . . .  . . . . .....  357
6.8 Dynamic Linear Models with Switching . . . . . . . . . .... 362
6.9 Nonlinear and Non-normal State-Space
Models Using Monte Carlo Methods . . . . . . . . . . . ....  376
6.10  Stochastic Volatility  ........  . . . . . . .  .  .  .  ... .   388
6.11 State-Space and ARMAX Models for
Longitudinal Data Analysis . . . . . . . .  .  .  .  .....  . 394
Problems . ... . ........................... ..404
7 Statistical Methods in the Frequency Domain                412
7.1  Introduction  ......... . . . . . . . . . . . .  . . . . . .  412
7.2 Spectral Matrices and Likelihood Functions . . . . . . . . ...  416
7.3 Regression for Jointly Stationary Series . . . . . . . . . ....  417
7.4 Regression with Deterministic Inputs . . . . . .  . . . .....  426
7.5 Random Coefficient Regression ..... . . . . . .  . . . . .....  434
7.6 Analysis of Designed Experiments . . . . . .  . . . . .....  438
7.7 Discrimination and Cluster Analysis . . . . . . . . . . . ....  449
7.8  Principal Components and Factor Analysis . . . . . . . . ...  464
7.9  The Spectral Envelope . . . . . . . . . . . .  .  .  .  .  .  .   . 479
Problems .......... ..... . ................ 495



Library of Congress subject headings for this publication: Time-series analysis, Tijdreeksen, gttToepassingen, gttSérie chronologique