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关键词：econometrics Econometric handbook metrics econom econometrics handbook

Chapter 49
ARCH MODELS”
TIM BOLLERSLEV
Northwestern University and N.B.E.R.
ROBERT F. ENGLE
University of California, San Diego and N.B.E.R.
DANIEL B. NELSON
University of Chicago and N.B.E.R.
Contents
Abstract
1. Introduction
1.1. Definitions
1.2. Empirical regularities of asset returns
1.3. Univariate parametric models
1.4. ARCH in mean models
1.5. Nonparametric and semiparametric methods
2. Inference procedures
2.1. Testing for ARCH
2.2. Maximum likelihood methods
2.3. Quasi-maximum likelihood methods
2.4. Specification checks
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“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 GAUSSTM code used in the
stock market empirical example is available from Inter-University Consortium for Political and Social
Research (ICPSR), P.O. Box 1248, Ann Arbor, MI 48106, USA, telephone (313)763-5010. Order
“Class 5” under this article’s name.
Handbook ofEconometrics, VolumeChapter 49
ARCH MODELS”
TIM BOLLERSLEV
Northwestern University and N.B.E.R.
ROBERT F. ENGLE
University of California, San Diego and N.B.E.R.
DANIEL B. NELSON
University of Chicago and N.B.E.R.
Contents
Abstract
1. Introduction
1.1. Definitions
1.2. Empirical regularities of asset returns
1.3. Univariate parametric models
1.4. ARCH in mean models
1.5. Nonparametric and semiparametric methods
2. Inference procedures
2.1. Testing for ARCH
2.2. Maximum likelihood methods
2.3. Quasi-maximum likelihood methods
2.4. Specification checks
3. Stationary and ergodic properties
3.1. Strict stationarity
3.2. Persistence
4. Continuous time methods
4.1. ARCH models as approximations to diffusions
4.2. Diffusions as approximations to ARCH models
4.3, ARCH models as filters and forecasters
5. Aggregation and forecasting
5.1. Temporal aggregation
5.2. Forecast error distributions
6. Multivariate specifications
6.1. Vector ARCH and diagonal ARCH
6.2. Factor ARCH
6.3. Constant conditional correlations
6.4. Bivariate EGARCH
6.5. Stationarity and co-persistence
7. Model selection
8. Alternative measures for volatility
9. Empirical examples
9.1. U.S. Dollar/Deutschmark exchange rates
9.2. U.S. stock prices
10. Conclusion