Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T11:38:39.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Multivariate Simultaneous Generalized ARCH

Published online by Cambridge University Press:  11 February 2009

Robert F. Engle  and
Kenneth F. Kroner
Robert F. Engle
Affiliation:
University of California, San Diego
Kenneth F. Kroner
Affiliation:
University of Arizona
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper presents theoretical results on the formulation and estimation of multivariate generalized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed, and equivalence relations are discussed for the various ARCH parameterizations. Constraints sufficient to guarantee the positive definiteness of the conditional covariance matrices are developed, and necessary and sufficient conditions for covariance stationarity are presented. Identification and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 1 , February 1995 , pp. 122 - 150
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Berndt, E.K., Hall, B.H., Hall, R.E. & Hausman, J.A. (1974) Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement 3/4, 653–665.Google Scholar
Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–328.CrossRefGoogle Scholar
Bollerslev, T., Chou, R.Y. & Kroner, K.F. (1992) ARCH modeling in finance: A review of the theory and empirical evidence. Journal of Econometrics 52, 5–59.CrossRefGoogle Scholar
Bollerslev, T., Engle, R.F. & Wooldridge, J.M. (1988) A capital asset pricing model with time varying covariances. Journal of Political Economy 96, 116–131.CrossRefGoogle Scholar
Bollerslev, T. & Wooldridge, J.M. (1992) Quasi maximum likelihood estimation and inference in dynamic models with time varying covariances. Econometric Reviews 11, 143–172.CrossRefGoogle Scholar
Dhrymes, P.J. (1984) Mathematics for Econometrics, 2nd ed.New York: Springer-Verlag.CrossRefGoogle Scholar
Engel, C. & Rodrigues, A.P. (1989) Tests of international CAPM with time varying covariances. Journal of Applied Econometrics 4, 119–128.CrossRefGoogle Scholar
Engle, R.F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.CrossRefGoogle Scholar
Engle, R.F., Granger, C.W.J. & Kraft, D.F. (1984) Combining competing forecasts of inflation using a bivariate ARCH model. Journal of Economic Dynamics and Control 8, 151–165.CrossRefGoogle Scholar
Engle, R.F., Hendry, D.F. & Richard, J.-F. (1983) Exogeneity. Econometrica 51, 277–304.CrossRefGoogle Scholar
Friedman, M. (1977) Nobel lecture: Inflation and unemployment. Journal of Political Economy 85, 451–472.CrossRefGoogle Scholar
Kaminsky, G.L. & Peruga, R. (1990) Can a time varying risk premium explain excess returns in the forward market for foreign exchange? Journal of International Economics 28, 47–70.CrossRefGoogle Scholar
Kraft, D.F. & Engle, R.F. (1983) Autoregressive Conditional Heteroskedasticity in Multiple Time Series Models. Unpublished manuscript, Department of Economics, University of California, San Diego.Google Scholar
Kroner, K.F. & Claessens, S. (1991) Optimal dynamic hedging portfolios and the currency composition of external debt. Journal of International Money and Finance 10, 131–148.CrossRefGoogle Scholar
Kroner, K.F. & Lastrapes, W.D. (1993) The impact of exchange rate volatility on international trade: Estimates using the GARCH-M model. Journal of International Money and Finance 12, 298–318.CrossRefGoogle Scholar
Kroner, K.F. & Sultan, J. (1993) Time-varying distributions and dynamic hedging with foreign currency futures. Journal of Financial and Quantitative Analysis 28, 535–551.CrossRefGoogle Scholar
Lee, S.-W. & Hansen, B.E. (1994) Asymptotic theory for the GARCH(1,1) quasi-maximum likelihood estimator. Econometric Theory 10, 29–52.CrossRefGoogle Scholar
Lumsdaine, R.L. (1991) Asymptotic Properties of the Quasi-Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models. Unpublished manuscript, Princeton University and National Bureau of Economic Research.Google Scholar
McCurdy, T.H. & Morgan, I.G. (1988) Testing the martingale hypothesis in Deutschmark futures with models specifying the form of heteroskedasticity. Journal of Applied Econometrics 3, 187–202.CrossRefGoogle Scholar
McCurdy, T.H. & Morgan, I.G. (1991) Tests for systematic risk components in deviations from uncovered interest rate parity. Review of Economic Studies 58, 587–602.CrossRefGoogle Scholar
Pagan, A.R. & Sabau, H.C.L. (1987) On the Inconsistency of the MLE in Certain Heteroskedastic Regression Models. Unpublished manuscript, Department of Economics, University of Rochester.Google Scholar
Weiss, A.A. (1986) Asymptotic theory for ARCH models: Estimation and testing. Econometric Theory 2, 107–131.CrossRefGoogle Scholar