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Handbook of Econometrics Vols1-5 _ Chapter 48

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Chapter 48 ASPECTS OF MODELLING TIM0 TERASVIRTA NONLINEAR TIME SERIES* Contents Abstract 1. Introduction 2. Types of nonlinear models theory models parameter and long-memory model Models from time series theory Flexible statistical State-dependent, Nonparametric parametric time-varying models | Chapter 48 ASPECTS OF MODELLING NONLINEAR TIME SERIES TIMO TERASVIRTA Copenhagen Business School and Bank of Norway DAG TJ0STHEIM 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 2927 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 The work for this paper originated when TT and DT were visiting the University of California San Diego. They wish to thank the economics and mathematics departments respectively of UCSD for their hospitality and John Rice and Murray Rosenblatt in particular. The research of TT was also supported by the University of Göteborg Bank of Norway and a grant from the Yrjö Jahnsson Foundation. DT acknowledges financial support from the Norwegian Council for Research and CWJG from NSF Grant SES 9023037. Handbook of Econometrics Volume IV Edited by R.F. Engle and D.L. McFadden 1994 Elsevier Science B.V. All rights reserved 2918 T. Teràsvirta et al. 5.2. Estimation of nonparametric functions 5.3. Estimation of restricted nonparametric and semiparametric models 6. Evaluation of estimated models 7. Example 8. Conclusions References 2938 2942 2945 2946 2952 2953 Ch. 48 Aspects of Modelling Nonlinear Time Series 2919 Abstract This paper surveys some of the recent developments in nonlinear analysis of economic time series. The emphasis lies on stochastic models. Various classes of nonlinear models appearing in the economics and time series literature are presented and discussed. .