Cover --
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