http://repub.eur.nl/res/aut/6422/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/1833/ 2009-01-28T00:00:00Z In this paper we examine the usefulness of multivariate semi-parametric GARCH models for evaluating the Value-at-Risk (VaR) of a portfolio with arbitrary weights. We specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations. http://repub.eur.nl/res/pub/1480/ 2004-08-12T00:00:00Z 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 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. 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. http://repub.eur.nl/res/pub/1286/ 2004-05-21T00:00:00Z Estimation of multivariate volatility models is usually carried out by quasi maximum likelihood (QMLE), for which consistency and asymptotic normality have been proven under quite general conditions. However, there may be a substantial efficiency loss of QMLE if the true innovation distribution is not multinormal. We suggest a nonparametric estimation of the multivariate innovation distribution, based on consistent parameter estimates obtained by QMLE. We show that under standard regularity conditions the semiparametric efficiency bound can be attained. Without reparametrizing the conditional covariance matrix (which depends on the particular model used), adaptive estimation is not possible. However, in some cases the efficiency loss of semiparametric estimation with respect to full information maximum likelihood decreases as the dimension increases. In practice, one would like to restrict the class of possible density functions to avoid the curse of dimensionality. One way of doing so is to impose the constraint that the density belongs to the class of spherical distributions, for which we also derive the semiparametric efficiency bound and an estimator that attains this bound. A simulation experiment demonstrates the efficiency gain of the proposed estimator compared with QMLE.