Chapter 48
ASPECTS OF MODELLING NONLINEAR TIME SERIES*
TIM0 TERASVIRTA
Copenhagen Business School and Bank of Norway
DAG TJ@STHEIM
University of Bergen
CLIVE W.J. GRANGER
University of California
Contents
Abstract 2919
1. Introduction 2919
2. Types of nonlinear models 2921
2.1. Models from economic theory 2921
2.2. Models from time series theory 2922
2.3. Flexible statistical parametric models 2923
2.4. State-dependent, time-varying parameter and long-memory models 2924
2.5. Nonparametric models 2925
3. Testing linearity 2926
3.1. Tests against a specific alternative 2921
3.2. Tests without a specific alternative 2930
3.3. Constancy of conditional variance 2933
4. Specification of nonlinear models 2934
5. Estimation in nonlinear time series 2937
5.1. Estimation of parameters in parametric models 2937
5.2. Estimation of nonparametric functions 2938
5.3. Estimation of restricted nonparametric and semiparametric models 2942
6. Evaluation of estimated models 2945
7. Example 2946
8. Conclusions 2952
References 2953