مقدمه ای بر سری های زمانی و پیش بینی

Table of Contents —

Preface —

Chapter 1. Introduction —

1.1. Examples of Time Series —

1.2. Objectives of Time Series Analysis —

1.3. Some Simple Time Series Models —

1.4. Stationary Models and the Autocorrelation Function —

1.5. Estimation and Elimination of Trend and Seasonal Components —

1.6. Testing the Estimated Noise Sequence —

Problems —

Chapter 2. Stationary Processes —

2.1. Basic Properties —

2.2. Linear Processes —

2.3. Introduction to ARMA Processes —

2.4. Properties of the Sample Mean and Autocorrelation Function —

2.5. Forecasting Stationary Time Series —

2.6. The Wold Decomposition —

Problems —

Chapter 3. ARMA Models —

3.1. ARMA(p, q) Processes —

3.2. The ACF and PACF of an ARMA(p, q) Process —

3.3. Forecasting ARMA Processes —

Problems —

Chapter 4. Spectral Analysis —

4.1. Spectral Densities —

4.2. The Periodogram —

4.3. Time-Invariant Linear Filters —

4.4. The Spectral Density of an ARMA Process —

Problems —

Chapter 5. Modeling and Forecasting with ARMA Processes —

5.1. Preliminary Estimation —

5.2. Maximum Likelihood Estimation —

5.3. Diagnostic Checking —

5.4. Forecasting —

5.5. Order Selection —

Problems —

Chapter 6. Nonstationary and Seasonal Time Series Models —

6.1. ARIMA Models for Nonstationary Time Series —

6.2. Identification Techniques —

6.3. Unit Roots in Time Series Models —

6.4. Forecasting ARIMA Models —

6.5. Seasonal ARIMA Models —

6.6. Regression with ARMA Errors —

Problems —

Chapter 7. Multivariate Time Series —

7.1. Examples —

7.2. Second-Order Properties of Multivariate Time Series —

7.3. Estimation of the Mean and Covariance Function —

7.4. Multivariate ARMA Processes —

7.5. Best Linear Predictors of Second-Order Random Vectors —

7.6. Modeling and Forecasting with Multivariate AR Processes —

7.7. Cointegration —

Problems —

Chapter 8. State-Space Models —

8.1. State-Space Representations —

8.2. The Basic Structural Model —

8.3. State-Space Representation of ARIMA Models —

8.4. The Kalman Recursions —

8.5. Estimation For State-Space Models —

8.6. State-Space Models with Missing Observations —

8.7. The EM Algorithm —

8.8. Generalized State-Space Models —

Problems —

Chapter 9. Forecasting Techniques —

9.1. The ARAR Algorithm —

9.2. The Holt … Winters Algorithm —

9.3. The Holt … Winters Seasonal Algorithm —

9.4. Choosing a Forecasting Algorithm —

Problems —

Chapter 10. Further Topics —

10.1. Transfer Function Models —

10.2. Intervention Analysis —

10.3. Nonlinear Models —

10.4. Continuous-Time Models —

10.5. Long-Memory Models —

Problems —

Appendix A. Random Variables and Probability Distributions —

A.1. Distribution Functions and Expectation —

A.2. Random Vectors —

A.3. The Multivariate Normal Distribution —

Problems —

Appendix B. Statistical Complements —

B.1. Least Squares Estimation —

B.2. Maximum Likelihood Estimation —

B.3. Confidence Intervals —

B.4. Hypothesis Testing —

Appendix C. Mean Square Convergence —

C.1. The Cauchy Criterion