Introduction to Time Series and Forecasting.pdf

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作者Peter J. Brockwell Richard A. Davis
现给出部分目录如下
Contents
1.  Introduction 1
1.1.  Examples of Time Series 1
1.2.  Objectives of Time Series Analysis 6
1.3.  Some Simple Time Series Models 7
1.3.1. Some Zero-Mean Models 8
1.3.2. Models with Trend and Seasonality 9
1.3.3. A General Approach to Time Series Modeling 14
1.4.  Stationary Models and the Autocorrelation Function 15
1.4.1. The Sample Autocorrelation Function 18
1.4.2. A Model for the Lake Huron Data 21
1.5.  Estimation and Elimination of Trend and Seasonal Components          23
1.5.1. Estimation and Elimination of Trend in the Absence of
Seasonality 24
1.5.2. Estimation and Elimination of Both Trend and
Seasonality 31
1.6.  Testing the Estimated Noise Sequence 35
Problems 40
2.  Stationary Processes 45
2.1.  Basic Properties 45
2.2.  Linear Processes 51
2.3.  Introduction to ARMA Processes 55
2.4.  Properties of the Sample Mean and Autocorrelation Function 57
2.4.1. Estimation of µ
58
2.4.2. Estimation of γ (·) and ρ(·)
59
2.5.  Forecasting Stationary Time Series 63
2.5.1. The Durbin–Levinson Algorithm 69
2.5.2. The Innovations Algorithm 71
2.5.3. Prediction of a Stationary Process in Terms of Infinitely
Many Past Values 75
3.  ARMA Models 83
3.1.  ARMA(p, q) Processes 83
3.2.  The ACF and PACF of an ARMA(p, q) Process 88
3.2.1. Calculation of the ACVF 88
3.2.2. The Autocorrelation Function 94
3.2.3. The Partial Autocorrelation Function 94
3.2.4. Examples 96
3.3.  Forecasting ARMA Processes 100
Problems 108
4.  Spectral Analysis 111
4.1.  Spectral Densities 112
4.2.  The Periodogram 121
4.3.  Time-Invariant Linear Filters 127
4.4.  The Spectral Density of an ARMA Process 132
Problems 134
5.  Modeling and Forecasting with ARMA Processes 137
5.1.  Preliminary Estimation 138
5.1.1. Yule–Walker Estimation 139
5.1.2. Burg’s Algorithm 147
5.1.3. The Innovations Algorithm 150
5.1.4. The Hannan–Rissanen Algorithm 156
5.2.  Maximum Likelihood Estimation 158
5.3.  Diagnostic Checking 164
5.3.1. The Graph of
ˆRt , t  1, . . . , n
165
5.3.2. The Sample ACF of the Residuals 166
5.3.3. Tests for Randomness of the Residuals 166
5.4.  Forecasting 167
5.5.  Order Selection 169
5.5.1. The FPE Criterion 170
5.5.2. The AICC Criterion 171
Problems 174
6.  Nonstationary and Seasonal Time Series Models 179
6.1.  ARIMA Models for Nonstationary Time Series 180
6.2.  Identification Techniques 187
6.3.  Unit Roots in Time Series Models 193
6.3.1. Unit Roots in Autoregressions 194
6.3.2. Unit Roots in Moving Averages 196
6.4.  Forecasting ARIMA Models 198
6.4.1. The Forecast Function 200
6.5.  Seasonal ARIMA Models 203
6.5.1. Forecasting SARIMA Processes 208
6.6.  Regression with ARMA Errors 210
6.6.1. OLS and GLS Estimation 210
6.6.2. ML Estimation 213
Problems 219
7.  Multivariate Time Series 223
7.1.  Examples 224
7.2.  Second-Order Properties of Multivariate Time Series 229
7.3.  Estimation of the Mean and Covariance Function 234
7.3.1. Estimation of µ
234
7.3.2. Estimation of
(h)
235
7.3.3. Testing for Independence of Two Stationary Time Series         237
7.3.4. Bartlett’s Formula 238
7.4.  Multivariate ARMA Processes 241
7.4.1. The Covariance Matrix Function of a Causal ARMA
Process 244
7.5.  Best Linear Predictors of Second-Order Random Vectors 244
7.6.  Modeling and Forecasting with Multivariate AR Processes 246
7.6.1. Estimation for Autoregressive Processes Using Whittle’s
Algorithm 247
7.6.2. Forecasting Multivariate Autoregressive Processes 250
7.7.  Cointegration 254
Problems 256
8.  State-Space Models 259
8.1.  State-Space Representations 260
8.2.  The Basic Structural Model 263
8.3.  State-Space Representation of ARIMA Models 267
8.4.  The Kalman Recursions 271
8.5.  Estimation For State-Space Models 277
8.6.  State-Space Models with Missing Observations 283
8.7.  The EM Algorithm 289
8.8.  Generalized State-Space Models 292
8.8.1. Parameter-Driven Models 292xii
Contents
8.8.2. Observation-Driven Models 299
Problems 311
9.  Forecasting Techniques 317
9.1.  The ARAR Algorithm 318
9.1.1. Memory Shortening 318
9.1.2. Fitting a Subset Autoregression 319
9.1.3. Forecasting 320
9.1.4. Application of the ARAR Algorithm 321
9.2.  The Holt–Winters Algorithm 322
9.2.1. The Algorithm 322
9.2.2. Holt–Winters and ARIMA Forecasting 324
9.3.  The Holt–Winters Seasonal Algorithm 326
9.3.1. The Algorithm 326
9.3.2. Holt–Winters Seasonal and ARIMA Forecasting 328
9.4.  Choosing a Forecasting Algorithm 328
Problems 330
10.  Further Topics 331
10.1.  Transfer Function Models 331
10.1.1. Prediction Based on a Transfer Function Model 337
10.2.  Intervention Analysis 340
10.3.  Nonlinear Models 343
10.3.1. Deviations from Linearity 344
10.3.2. Chaotic Deterministic Sequences 345
10.3.3. Distinguishing Between White Noise and iid Sequences        347
10.3.4. Three Useful Classes of Nonlinear Models 348
10.3.5. Modeling Volatility 349
10.4.  Continuous-Time Models 357
10.5.  Long-Memory Models 361
Problems 365

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