时间序列的理论与方法 第2版 英文PDF电子书下载

CHAPTER 1 Stationary Time Series 1

1.1 Examples of Time Series 1

1.2 Stochastic Processes 8

1.3 Stationarity and Strict Stationarity 11

1.4 The Estimation and Elimination of Trend and Seasonal Components 14

1.5 The Autocovariance Function of a Stationary Process 25

1.6 The Multivariate Normal Distribution 32

1.7 Applications of Kolmogorov's Theorem 37

Problems 39

CHAPTER 2 Hilbert Spaces 42

2.1 Inner-Product Spaces and Their Properties 42

2.2 Hilbert Spaces 46

2.3 The Projection Theorem 48

2.4 Orthonormal Sets 54

2.5 Projection in Rn 58

2.6 Linear Regression and the General Linear Model 60

2.7 Mean Square Convergence,Conditional Expectation and Best Linear Prediction in L2(？,？,P) 62

2.8 Fourier Series 65

2.9 Hilbert Space Isomorphisms 67

2.10 The Completeness of L2(？,？,P) 68

2.11 Complementary Results for Fourier Series 69

Problems 73

CHAPTER 3 Stationary ARMA Processes 77

3.1 Causal and Invertible ARMA Processes 77

3.2 Moving Average Processes of Infinite Order 89

3.3 Computing the Autocovariance Function of an ARMA(p,q)Process 91

3.4 The Partial Autocorrelation Function 98

3.5 The Autocovariance Generating Function 103

3.6 Homogeneous Linear Difference Equations with Constant Coefficients 105

Problems 110

CHAPTER 4 The Spectral Representation of a Stationary Process 114

4.1 Complex-Valued Stationary Time Series 114

4.2 The Spectral Distribution of a Linear Combination of Sinusoids 116

4.3 Herglotz's Theorem 117

4.4 Spectral Densities and ARMA Processes 122

4.5 Circulants and Their Eigenvalues 133

4.6 Orthogonal Increment Processes on[-π,π] 138

4.7 Integration with Respect to an Orthogonal Increment Process 140

4.8 The Spectral Representation 143

4.9 Inversion Formulae 150

4.10 Time-Invariant Linear Filters 152

4.11 Properties of the Fourier Approximation hn to I(ν,ω] 157

Problems 159

CHAPTER 5 Prediction of Stationary Processes 166

5.1 The Prediction Equations in the Time Domain 166

5.2 Recursive Methods for Computing Best Linear Predictors 169

5.3 Recursive Prediction of an ARMA(p,q)Process 175

5.4 Prediction of a Stationary Gaussian Process;Prediction Bounds 182

5.5 Prediction of a Causal Invertible ARMA Process in Terms of Xj,-∞<j≤n 182

5.6 Prediction in the Frequency Domain 185

5.7 The Wold Decomposition 187

5.8 Kolmogorov's Formula 191

Problems 192

CHAPTER 6 Asymptotic Theory 198

6.1 Convergence in Probability 198

6.2 Convergence in rth Mean,r>0 202

6.3 Convergence in Distribution 204

6.4 Central Limit Theorems and Related Results 209

Problems 215

CHAPTER 7 Estimation of the Mean and the Autocovariance Function 218

7.1 Estimation of μ 218

7.2 Estimation of γ(·)andρ(·) 220

7.3 Derivation of the Asymptotic Distributions 225

Problems 236

CHAPTER 8 Estimation for ARMA Models 238

8.1 The Yule-Walker Equations and Parameter Estimation for Autoregressive Processes 239

8.2 Preliminary Estimation for Autoregressive Processes Using the Durbin-Levinson Algorithm 241

8.3 Preliminary Estimation for Moving Average Processes Using the Innovations Algorithm 245

8.4 Preliminary Estimation for ARMA(p,q)Processes 250

8.5 Remarks on Asymptotic Efficiency 253

8.6 Recursive Calculation of the Likelihood of an Arbitrary Zero-Mean Gaussian Process 254

8.7 Maximum Likelihood and Least Squares Estimation for ARMA Processes 256

8.8 Asymptotic Properties of the Maximum Likelihood Estimators 258

8.9 Confidence Intervals for the Parameters of a Causal Invertible ARMA Process 260

8.10 Asymptotic Behavior of the Yule-Walker Estimates 262

8.11 Asymptotic Normality of Parameter Estimators 265

Problems 269

CHAPTER 9 Model Building and Forecasting with ARIMA Processes 273

9.1 ARIMA Models for Non-Stationary Time Series 274

9.2 Identification Techniques 284

9.3 Order Selection 301

9.4 Diagnostic Checking 306

9.5 Forecasting ARIMA Models 314

9.6 Seasonal ARIMA Models 320

Problems 326

CHAPTER 10 Inference for the Spectrum of a Stationary Process 330

10.1 The Periodogram 331

10.2 Testing for the Presence of Hidden Periodicities 334

10.3 Asymptotic Properties of the Periodogram 342

10.4 Smoothing the Periodogram 350

10.5 Confidence Intervals for the Spectrum 362

10.6 Autoregressive,Maximum Entropy,Moving Average and Maximum Likelihood ARMA Spectral Estimators 365

10.7 The Fast Fourier Transform(FFT)Algorithm 373

10.8 Derivation of the Asymptotic Behavior of the Maximum Likelihood and Least Squares Estimators of the Coefficients of an ARMA Process 375

Problems 396

CHAPTER 11 Multivariate Time Series 401

11.1 Second Order Properties of Multivariate Time Series 402

11.2 Estimation of the Mean and Covariance Function 405

11.3 Multivariate ARMA Processes 417

11.4 Best Linear Predictors of Second Order Random Vectors 421

11.5 Estimation for Multivariate ARMA Processes 430

11.6 The Cross Spectrum 434

11.7 Estimating the Cross Spectrum 443

11.8 The Spectral Representation of a Multivariate Stationary Time Series 454

Problems 459

CHAPTER 12 State-Space Models and the Kalman Recursions 463

12.1 State-Space Models 463

12.2 The Kalman Recursions 474

12.3 State-Space Models with Missing Observations 482

12.4 Controllability and Observability 489

12.5 Recursive Bayesian State Estimation 498

Problems 501

CHAPTER 13 Further Topics 506

13.1 Transfer Function Modelling 506

13.2 Long Memory Processes 520

13.3 Linear Processes with Infinite Variance 535

13.4 Threshold Models 545

Problems 552

Appendix:Data Sets 555

Bibliography 561

Index 567