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.

multivariate GARCH, temporal aggregation, weak GARCH
Semiparametric and Nonparametric Methods (jel C14), Time-Series Models; Dynamic Quantile Regressions (jel C22)
Econometric Institute Research Papers
Report / Econometric Institute, Erasmus University Rotterdam
Erasmus School of Economics

Hafner, C.M, & Rombouts, J.V.K. (2004). Estimation of temporally aggregated multivariate GARCH models (No. EI 2004-30). Report / Econometric Institute, Erasmus University Rotterdam. Retrieved from