Ebook: Introduction to time series and forecasting

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