Estimation of temporally aggregated multivariate GARCH models
This paper investigates the performance of quasi maximum likelihood (QML) and nonlinear least squares (NLS) estimation applied to temporally aggregated GARCH models. Since these are known to be only weak GARCH, the conditional variance of the aggregated process is in general not known. Thus, one major condition that is often used in proving the consistency of QML, the correct specification of the first two moments, is absent. Indeed, our results illustrate suggest that QML is not consistent, with a substantial bias if both the initial degree of persistence and the aggregation level are high. In other cases, QML might be taken as an approximation with only a small bias. Based on results for univariate GARCH models, NLS is likely to be consistent, although inefficient, for weak GARCH models. However, our simulation study reveals that NLS does not reduce the bias of QML in considerably large samples. As the variation of NLS estimates is much higher than that of QML, one would clearly prefer QML in most practical situations. An empirical example illustrates some of the results.
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- Drost, F.C. & Nijman, T.E., 1992.
"Temporal Aggregation of Garch Processes,"
9240, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper 1990-66, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
- Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
- Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006.
"Multivariate GARCH models: a survey,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
- BAUWENS, Luc & LAURENT, SÃ©bastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BAUWENS, Luc & LAURENT, SÃ©bastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP 1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
- HAFNER, Christian & ROMBOUTS, Jeroen, 2003. "Semiparametric multivariate GARCH models," CORE Discussion Papers 2003003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
- Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
- Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
- Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
- Christian Francq & Jean-Michel Zakoïan, 1997.
"Estimating Weak Garch Representations,"
97-40, Centre de Recherche en Economie et Statistique.
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