Handbook of Econometrics Vols1-5 _ Chapter 49

Chapter 49 ARCH MODELS” TIM BOLLERSLEV Northwestern University and . ROBERT F. ENGLE The authors would like to thank Torben G. Andersen, Patrick Billingsley, William A. Brock, Eric Ghysels, Lars P. Hansen, Andrew Harvey, Blake LeBaron, and Theo Nijman for helpful comments. | Chapter 49 ARCH MODELS3 TIM BOLLERSLEV Northwestern University and . ROBERT F. ENGLE University of California San Diego and . DANIEL B. NELSON University of Chicago and . Contents Abstract 2961 1. Introduction 2961 . Definitions 2961 . Empirical regularities of asset returns 2963 . Univariate parametric models 2967 . ARCH in mean models 2972 . Nonparametric and semiparametric methods 2972 2. Inference procedures 2974 . Testing for ARCH 2974 . Maximum likelihood methods 2977 . Quasi-maximum likelihood methods 2983 . Specification checks 2984 The authors would like to thank Torben G. Andersen Patrick Billingsley William A. Brock Eric Ghysels Lars P. Hansen Andrew Harvey Blake LeBaron and Theo Nijman for helpful comments. Financial support from the National Science Foundation under grants SES-9022807 Bollerslev SES-9122056 Engle and SES-9110131 and SES-9310683 Nelson and from the Center for Research in Security Prices Nelson is gratefully acknowledged. Inquiries regarding the data for the stock market empirical application should be addressed to Professor G. William Schwert Graduate School of Management University of Rochester Rochester NY 14627 USA. The GAUSS code used in the stock market empirical example is available from Inter-University Consortium for Political and Social Research ICPSR . Box 1248 Ann Arbor MI 48106 USA telephone 313 763-5010. Order Class 5 under this article s name. Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2960 T. Bollerslev et al. 3. Stationary and ergodic properties 2989 . Strict stationarity 2989 . Persistence 2990 4. Continuous time methods 2992 . ARCH models as approximations to diffusions 2994 . Diffusions as approximations to ARCH models 2996 . ARCH models as filters and forecasters 2997 5. Aggregation and forecasting 2999 . Temporal aggregation 2999 . Forecast error distributions 3001 6.