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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