New statistical methods and future directions of research in time series

A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include:

* Contributions from eleven of the worldâ??s leading figures in time series

* Shared balance between theory and application

* Exercise series sets

* Many real data examples

* Consistent style and clear, common notation in all contributions

* 60 helpful graphs and tables

Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis.

An Instructor's Manual presenting detailed solutions to all the problems in he book is available upon request from the Wiley editorial department.

GEORGE C. TIAO, PhD, is W. Allen Wallis Professor of Statistics and Econometrics, Graduate School of Business, University of Chicago.

RUEY S. TSAY, PhD, is H. G. B. Alexander Professor of Statistics and Econometrics, Graduate School of Business, University of Chicago.

New statistical methods and future directions of research in time series

A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include:

• Contributions from eleven of the worldâ??s leading figures in time series
• Shared balance between theory and application
• Exercise series sets
• Many real data examples
• Consistent style and clear, common notation in all contributions
• 60 helpful graphs and tables

Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis.

An Instructor's Manual presenting detailed solutions to all the problems in he book is available upon request from the Wiley editorial department.

1. Introduction 1
D. Pena and G. C. Tiao

1.1. Examples of time series problems, 1

1.1.1. Stationary series, 2

1.1.2. Nonstationary series, 3

1.1.3. Seasonal series, 5

1.1.4. Level shifts and outliers in time series, 7

1.1.5. Variance changes, 7

1.1.6. Asymmetric time series, 7

1.1.7. Unidirectional-feedback relation between series, 9

1.1.8. Comovement and cointegration, 10

1.2. Overview of the book, 10

1.3. Further reading, 19

PART I BASIC CONCEPTS IN UNIVARIATE TIME SERIES

2. Univariate Time Series: Autocorrelation, Linear Prediction, Spectrum, and State-Space Model 25
G. T. Wilson

2.1. Linear time series models, 25

2.2. The autocorrelation function, 28

2.3. Lagged prediction and the partial autocorrelation function, 33

2.4. Transformations to stationarity, 35

2.5. Cycles and the periodogram, 37

2.6. The spectrum, 42

2.7. Further interpretation of time series acf, pacf, and spectrum, 46

2.8. State-space models and the Kalman Filter, 48

3. Univariate Autoregressive Moving-Average Models 53
G. C. Tiao

3.1. Introduction, 53

3.1.1. Univariate ARMA models, 54

3.1.2. Outline of the chapter, 55

3.2. Some basic properties of univariate ARMA models, 55

3.2.1. The ø and TT weights, 56

3.2.2. Stationarity condition and autocovariance structure o f z 58

3.2.3. The autocorrelation function, 59

3.2.4. The partial autocorrelation function, 60

3.2.5. The extended autocorrelaton function, 61

3.3. Model specification strategy, 63

3.3.1. Tentative specification, 63

3.3.2. Tentative model specification via SEACF, 67

3.4. Examples, 68

4. Model Fitting and Checking, and the Kalman Filter 86
G. T. Wilson

4.1. Prediction error and the estimation criterion, 86

4.2. The likelihood of ARMA models, 90

4.3. Likelihoods calculated using orthogonal errors, 94

4.4. Properties of estimates and problems in estimation, 98

4.5. Checking the fitted model, 101

4.6. Estimation by fitting to the sample spectrum, 104

4.7. Estimation of structural models by the Kalman filter, 105

5. Prediction and Model Selection 111
D. Pefia

5.1. Introduction, 111

5.2. Properties of minimum mean-square error prediction, 112

5.2.1. Prediction by the conditional expectation, 112

5.2.2. Linear predictions, 113

5.3. The computation of ARIMA forecasts, 114

5.4. Interpreting the forecasts from ARIMA models, 116

5.4.1. Nonseasonal models, 116

5.4.2. Seasonal models, 120

5.5. Prediction confidence intervals, 123

5.5.1. Known parameter values, 123

5.5.2. Unknown parameter values, 124

5.6. Forecast updating, 125

5.6.1. Computing updated forecasts, 125

5.6.2. Testing model stability, 125

5.7. The combination of forecasts, 129

5.8. Model selection criteria, 131

5.8.1. The FPE and AIC criteria, 131

5.8.2. The Schwarz criterion, 133

5.9. Conclusions, 133

6. Outliers, Influential Observations, and Missing Data 136
D. Pena

6.1. Introduction, 136

6.2. Types of outliers in time series, 138

6.2.1. Additive outliers, 138

6.2.2. Innovative outliers, 141

6.2.3. Level shifts, 143

6.2.4. Outliers and intervention analysis, 146

6.3. Procedures for outlier identification and estimation, 147

6.3.1. Estimation of outlier effects, 148

6.3.2. Testing for outliers, 149

6.4. Influential observations, 152

6.4.1. Influence on time series, 152

6.4.2. Influentia...