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ON THE PARAMETRIZATION OF MULTIVARIATE GARCH MODELS

Published online by Cambridge University Press:  05 April 2007

Wolfgang Scherrer  and
Eva Ribarits
Wolfgang Scherrer
Affiliation:
Institute of Mathematical Methods in Economics, Vienna University of Technology
Eva Ribarits
Affiliation:
Institute of Mathematical Methods in Economics, Vienna University of Technology
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Abstract

This paper deals with issues of structure and parametrization of VECH models proposed in Bollerslev, Engle, and Wooldridge (1988) and Baba, Engle, Kraft, and Kroner (BEKK) models. Both general models and also restricted versions such as the widely used diagonal VECH (DVECH) and factor generalized autoregressive conditional heteroskedastic (F-GARCH) models are discussed. A simple algorithm is presented that checks whether a given VECH model may be cast as a BEKK model. It is shown that in the bivariate case BEKK models are as general as VECH models. In higher dimensional cases however, VECH models allow for more flexibility. In addition, a parametrization for a generic, i.e., open and dense, class of BEKK models is given, and the frequently cited parametrization by Engle and Kroner (1995, Econometric Theory 11, 122–150) is analyzed. Two shortcomings of the latter are pointed out. Finally, parametrizations for BEKK(p,q,K) models with K ≤ n, including DVECH, F-GARCH, and a generalization of the latter, are discussed.This research was supported by the project P17065 “Identification of multivariate dynamic systems with a focus on dimension reduction” of the Austrian Science Foundation (FWF).

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 3 , June 2007 , pp. 464 - 484
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Baba, Y., R.F. Engle, D.F. Kraft, & K.F. Kroner (1991) Multivariate simultaneous generalised ARCH. Discussion paper 89-57, University of California, San Diego, Department of Economics.
Bauwens, L., S. Laurent, & J.V. Rombout (2006) Multivariate GARCH models: A survey. Journal of Applied Econometrics 21, 79–109.Google Scholar
Bollerslev, T. (1986) Generalised autoregressive heteroscedasticity. Journal of Econometrics 31, 307–327.Google Scholar
Bollerslev, T., R. Engle, & D. Nelson (1994) ARCH models. In R. Engle & D. McFadden (eds.), Handbook of Econometrics, vol. 4, pp. 2959–3038. North-Holland.
Bollerslev, T., R. Engle, & J. Wooldridge (1988) A capital asset pricing model with time varying covariance. Journal of Political Economy 96, 116–131.Google Scholar
Engle, R. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of the U.K. inflation. Econometrica 50, 987–1008.Google Scholar
Engle, R.F. & K.F. Kroner (1995) Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150.Google Scholar
Engle, R., V. Ng, & M. Rothschild (1990) Asset pricing with a factor-ARCH covariance structure, empirical estimates for treasury bills. Journal of Econometrics 45, 213–237.Google Scholar
Harville, D.A. (1997) Matrix Algebra from a Statistician's Perspective. Springer-Verlag.
Pagan, A. (1996) The econometrics of financial markets. Journal of Empirical Finance 3, 15–102.Google Scholar
Palm, F. (1996) GARCH models of volatility. In G. Maddala & C. Rao (eds.), Handbook of Statistics, vol. 14, pp. 209–239. Elsevier.
Ribarits, E. (2006) Multivariate modeling of financial time series. Ph.D. dissertation, Vienna University of Technology.
Vandenberghe, L. & S. Boyd (1996) Semidefinite programming. SIAM Review 38, 49–95.Google Scholar