## Table of contents for Time series analysis : with applications in R / Jonathan D. Cryer, Kung-Sik Chan.

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```CHAPTER 1 INTRODUCTION .............................. 1
1.1  Examples of Time Series ...........................  1
1.2  A Model-Building Strategy .......................... 8
1.3  Time Series Plots in History .........................  8
1.4  An  Overview  of the  Book  .................... ........ 9
Exercises  ..................... ................ ......  10
CHAPTER 2 FUNDAMENTAL CONCEPTS .................. 11
2.1 Time Series and Stochastic Processes ................ 11
2.2  Means, Variances, and Covariances  .................. 11
2.3  Stationarity  .....................................  16
2.4  Summary  ....................................... 19
Exercises ...........................................  19
Appendix A: Expectation, Variance, Covariance, and Correlation. 24
CHAPTER 3 TRENDS ................................ 27
3.1  Deterministic Versus Stochastic Trends ................ 27
3.2  Estimation of a Constant Mean  ........... ............ 28
3.3  Regression Methods .............................. 30
3.4  Reliability and Efficiency of Regression Estimates........ 36
3.5  Interpreting  Regression Output ...................... 40
3.6  Residual Analysis ................................  42
3.7  Summary  ....................................... 50
Exercises  ................... ......................... 50
CHAPTER 4 MODELS FOR STATIONARY TIME SERIES..... 55
4.1  General Linear Processes  .......................... 55
4.2  Moving Average Processes ........................ 57
4.3  Autoregressive  Processes  .......................... 66
4.4  The Mixed Autoregressive Moving Average Model........ 77
4.5 Invertibility .................................... 79
4.6  Summary ..................................... 80
Exercises  ................... ......................... 81
Appendix B: The Stationarity Region for an AR(2) Process ..... 84
Appendix C: The Autocorrelation Function for ARMA(p,q). ...... 85
CHAPTER 5 MODELS FOR NONSTATIONARY TIME SERIES .87
5.1 Stationarity Through Differencing .....................88
5.2  ARIMA Models. ................. ................92
5.3  Constant Terms in ARIMA Models. ...........97
5.4  Other Transformations ..........................98
5.5  Summary ................................102
Exercises .........................................103
Appendix D: The Backshift Operator....................106
CHAPTER 6 MODEL SPECIFICATION...................109
6.1  Properties of the Sample Autocorrelation Function......
6.2 The Partial and Extended Autocorrelation Functions.....112
6.3  Specification of Some Simulated Time Series.........117
6.4  Nonstationarity...............................125
6.5  Other Specification Methods .....................130
6.6  Specification of Some Actual Time Series............133
6.7  Summary .................................141
Exercises.........................................141
CHAPTER 7 PARAMETER ESTIMATION .................149
7.1  The Method of Moments ........................149
7.2  Least Squares Estimation ............... .......154
7.3  Maximum Likelihood and Unconditional Least Squares ..158
7.4  Properties of the Estimates ......................160
7.5 Illustrations of Parameter Estimation ................163
7.6  Bootstrapping ARIMA Models ....................167
7.7  Summary ...................................170
Exercises .........................................170
CHAPTER 8 MODEL DIAGNOSTICS ....................175
8.1  Residual Analysis .........................175
8.2  Overfitting and Parameter Redundancy..............185
8.3  Summary ............................    ..188
Exercises......................................188
CHAPTER 9 FORECASTINGes ............................191
9.1 Minimum Mean Square Error Forecasting Transformed Series ...........191
9.9 Summary of Foministic Trecasting with Certain ARIM...........................191
9.103 ARIMA Forecastingy .............................193
Ex9.4   Prediction Limits..........  ..............203
9.5Appendix E: Conditional Expects .........................204
Appendix F: Minimum Mean Square Error Predicti
Appendix G: The Truncated Linear Process ....
9.6 UAppendix H: State Space Modelas ......................207
9.7 Forecast Weights and Exponentially Weighted
MovingHAPTER 10 SEASONAL MODELS.............................207
10.1 Seasting Transformed Series. ...............209
10.2 Multiplicative Seasonal ARMA Models. ....
10.3 Nonstationary Seasonal ARIMA Models ...
10.4 Model Specification, Fitting, and Checking..
109.9 Summary of Forecasting Seasonal Modwith Certain ARIMA Models.... 211s .
9.10.6 Summary ..................................213
Exercises .......................................213
3HAPTER 1 1 TIME SERIES REGRESSION MOD
App11.1 Intervendix E: Condition Analysis Expectation.....................218
Appendix F: Minimum Mean Square Error Prediction ........ 218
Appendix G: The Truncated Linear Process ............... 221
11.2Appendix H: State Space Models ............... .....222
CHA11.3 Spurious CorrelationAL MODELS.................227
10.1 Seasonal ARIMA Models .................. ....... 228
10.2 Multiplicative Seasonal ARMA Models. .............230
10.3 Nonstationary Seasonal ARIMA Models .............233
11.4 PrModel Specification, Fitting,ng and Stochastic Regression .........234
10.5 Forecasting Seasonal Models .................. .. 241
11.5 Summary ..................................246
Exercises.......................................246
CHAPTER 11 TIME SERIES REGRESSION MODELS ...... 249
11 .1 Intervention Analysis ................. ......... 249
11 .2 Outliers. ................. ................... .257
11.3 Spurious Correlation. ................. ......... 260
11 .4 Prewhitening and Stochastic Regression ............. 265
11 .5 Summary ................. ................. 273
Exercises.................,,................. .....274
CHAPTER 12 TIME SERIES MODELS OF
HETEROSCEDASTICITY .................... 277
12.1 Some Common Features of Financial Time Series....... 278
12.2 The ARCH(1) Model ...........................285
12.3 GARCH Models ...............................289
12.4  Maximum  Likelihood Estimation  ................... . 298
12.5 Model Diagnostics ................................301
12.6 Conditions for the Nonnegativity of the
Conditional Variances ..........................307
12.7  Some Extensions of the GARCH Model ............... 310
12.8 Another Example: The Daily USD/HKD Exchange Rates. .311
12.9 Summary ................................. 315
Exercises ...................... . ......................  316
Appendix I: Formulas for the Generalized Portmanteau Tests .. .318
CHAPTER 13 INTRODUCTION TO SPECTRAL ANALYSIS .... .319
13.1 Introduction .................................. 319
13.2  The  Periodogram  ........... ....................322
13.3 The Spectral Representation and Spectral Distribution ... 327
13.4 The Spectral Density ................... ......... 330
13.5 Spectral Densities for ARMA Processes ............... 332
13.6 Sampling Properties of the Sample Spectral Density ..... 340
13.7 Summary ............   ...................... 346
Exercises ....................................... 346
Appendix J: Orthogonality of Cosine and Sine Sequences .....349
CHAPTER 14 ESTIMATING THE SPECTRUM ............... 351
14.1  Smoothing the Spectral Density  ..................... 351
14.2 Bias and Variance ................. ........... 354
14.3 Bandwidth ................................... 355
14.4 Confidence Intervals for the Spectrum ..............356
14.5  Leakage and Tapering .............................358
14.6 Autoregressive Spectrum Estimation ................. 363
14.7  Examples with Simulated Data  ................... .. 364
14.8  Examples with Actual Data  ........................ 370
14.9  Other Methods of Spectral Estimation ................. 376
14.10Summary ............... .................. 378
Exercises ............................................378
Appendix K: Tapering and the Dirichlet Kernel ............... 381
CHAPTER 15 THRESHOLD MODELS .................... 383
15.1  Graphically  Exploring  Nonlinearity  ................... 384
15.2  Tests for Nonlinearity  .................. ......... 390
15.3 Polynomial Models Are Generally Explosive ........... 393
15.4 First-Order Threshold Autoregressive Models .......... 395
15.5 Threshold Models .............................. 399
15.6  Testing for Threshold Nonlinearity  ..............  .... 400
15.7 Estimation of a TAR Model ....................... 402
15.8 Model Diagnostics .............................411
15.9 Prediction .................................. 415
15.10Summary .................................. 420
Exercises ..........................  ....... ........ 420
Appendix L: The Generalized Portmanteau Test for TAR ...... 421
APPENDIX: AN INTRODUCTION TO R ................... 423
Introduction ............    ......................423
Chapter 1 R Commands ............................429
Chapter 2 R Commands .............................. 433
Chapter 3 R Commands .............................. 433
Chapter 4 R Commands .............................. 438
Chapter 5 R Commands .............................. 439
Chapter 6 R Commands ............................ 441
Chapter 7 R Commands .............................. 442
Chapter 8 R Commands .............................. 446
Chapter 9 R Commands ............................. 447
Chapter 10 R Commands  .............................. 450
Chapter 11 R Commands ...........................  451
Chapter 12 R Commands ........................... 457
Chapter 13 R Commands ........................... 460
Chapter 14 R Commands ...........................461
Chapter 15 R Commands ...............   .......... 462
New or Enhanced Functions in the TSA Library ............. 468
DATASET  INFORMATION   .........................471
BIBLIOGRAPHY .................................... 477

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Library of Congress subject headings for this publication: Time-series analysis Data processing, R (Computer program language)