时间序列的理论与方法 第2版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

时间序列的理论与方法 第2版 英文PDF格式电子书版下载

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CHAPTER 1 Stationary Time Series1

1.1 Examples of Time Series1

1.2 Stochastic Processes8

1.3 Stationarity and Strict Stationarity11

1.4 The Estimation and Elimination of Trend and Seasonal Components14

1.5 The Autocovariance Function of a Stationary Process25

1.6 The Multivariate Normal Distribution32

1.7 Applications of Kolmogorov's Theorem37

Problems39

CHAPTER 2 Hilbert Spaces42

2.1 Inner-Product Spaces and Their Properties42

2.2 Hilbert Spaces46

2.3 The Projection Theorem48

2.4 Orthonormal Sets54

2.5 Projection in Rn58

2.6 Linear Regression and the General Linear Model60

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

2.8 Fourier Series65

2.9 Hilbert Space Isomorphisms67

2.10 The Completeness of L2(？,？,P)68

2.11 Complementary Results for Fourier Series69

Problems73

CHAPTER 3 Stationary ARMA Processes77

3.1 Causal and Invertible ARMA Processes77

3.2 Moving Average Processes of Infinite Order89

3.3 Computing the Autocovariance Function of an ARMA(p,q)Process91

3.4 The Partial Autocorrelation Function98

3.5 The Autocovariance Generating Function103

3.6 Homogeneous Linear Difference Equations with Constant Coefficients105

Problems110

CHAPTER 4 The Spectral Representation of a Stationary Process114

4.1 Complex-Valued Stationary Time Series114

4.2 The Spectral Distribution of a Linear Combination of Sinusoids116

4.3 Herglotz's Theorem117

4.4 Spectral Densities and ARMA Processes122

4.5 Circulants and Their Eigenvalues133

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

4.7 Integration with Respect to an Orthogonal Increment Process140

4.8 The Spectral Representation143

4.9 Inversion Formulae150

4.10 Time-Invariant Linear Filters152

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

Problems159

CHAPTER 5 Prediction of Stationary Processes166

5.1 The Prediction Equations in the Time Domain166

5.2 Recursive Methods for Computing Best Linear Predictors169

5.3 Recursive Prediction of an ARMA(p,q)Process175

5.4 Prediction of a Stationary Gaussian Process;Prediction Bounds182

5.5 Prediction of a Causal Invertible ARMA Process in Terms of Xj,-∞<j≤n182

5.6 Prediction in the Frequency Domain185

5.7 The Wold Decomposition187

5.8 Kolmogorov's Formula191

Problems192

CHAPTER 6 Asymptotic Theory198

6.1 Convergence in Probability198

6.2 Convergence in rth Mean,r>0202

6.3 Convergence in Distribution204

6.4 Central Limit Theorems and Related Results209

Problems215

CHAPTER 7 Estimation of the Mean and the Autocovariance Function218

7.1 Estimation of μ218

7.2 Estimation of γ(·)andρ(·)220

7.3 Derivation of the Asymptotic Distributions225

Problems236

CHAPTER 8 Estimation for ARMA Models238

8.1 The Yule-Walker Equations and Parameter Estimation for Autoregressive Processes239

8.2 Preliminary Estimation for Autoregressive Processes Using the Durbin-Levinson Algorithm241

8.3 Preliminary Estimation for Moving Average Processes Using the Innovations Algorithm245

8.4 Preliminary Estimation for ARMA(p,q)Processes250

8.5 Remarks on Asymptotic Efficiency253

8.6 Recursive Calculation of the Likelihood of an Arbitrary Zero-Mean Gaussian Process254

8.7 Maximum Likelihood and Least Squares Estimation for ARMA Processes256

8.8 Asymptotic Properties of the Maximum Likelihood Estimators258

8.9 Confidence Intervals for the Parameters of a Causal Invertible ARMA Process260

8.10 Asymptotic Behavior of the Yule-Walker Estimates262

8.11 Asymptotic Normality of Parameter Estimators265

Problems269

CHAPTER 9 Model Building and Forecasting with ARIMA Processes273

9.1 ARIMA Models for Non-Stationary Time Series274

9.2 Identification Techniques284

9.3 Order Selection301

9.4 Diagnostic Checking306

9.5 Forecasting ARIMA Models314

9.6 Seasonal ARIMA Models320

Problems326

CHAPTER 10 Inference for the Spectrum of a Stationary Process330

10.1 The Periodogram331

10.2 Testing for the Presence of Hidden Periodicities334

10.3 Asymptotic Properties of the Periodogram342

10.4 Smoothing the Periodogram350

10.5 Confidence Intervals for the Spectrum362

10.6 Autoregressive,Maximum Entropy,Moving Average and Maximum Likelihood ARMA Spectral Estimators365

10.7 The Fast Fourier Transform(FFT)Algorithm373

10.8 Derivation of the Asymptotic Behavior of the Maximum Likelihood and Least Squares Estimators of the Coefficients of an ARMA Process375

Problems396

CHAPTER 11 Multivariate Time Series401

11.1 Second Order Properties of Multivariate Time Series402

11.2 Estimation of the Mean and Covariance Function405

11.3 Multivariate ARMA Processes417

11.4 Best Linear Predictors of Second Order Random Vectors421

11.5 Estimation for Multivariate ARMA Processes430

11.6 The Cross Spectrum434

11.7 Estimating the Cross Spectrum443

11.8 The Spectral Representation of a Multivariate Stationary Time Series454

Problems459

CHAPTER 12 State-Space Models and the Kalman Recursions463

12.1 State-Space Models463

12.2 The Kalman Recursions474

12.3 State-Space Models with Missing Observations482

12.4 Controllability and Observability489

12.5 Recursive Bayesian State Estimation498

Problems501

CHAPTER 13 Further Topics506

13.1 Transfer Function Modelling506

13.2 Long Memory Processes520

13.3 Linear Processes with Infinite Variance535

13.4 Threshold Models545

Problems552

Appendix:Data Sets555

Bibliography561

Index567