FINITE-SAMPLE PROPERTIES OF THE MAXIMUM-LIKELIHOOD ESTIMATOR IN GARCH(1,1) AND IGARCH(1,1) MODELS - A MONTE-CARLO INVESTIGATION

This article compares GARCH(1,1) and IGARCH(1,1) models via a Monte Ca rlo study of the finite-sample properties of the maximum likelihood es timator and related test statistics. Although the asymptotic distribut ion is well approximated by the estimated t statistics, other commonly used statistics do not behave as well. In addition, the estimators th emselves are skewed in small samples. For the null hypothesis of IGARC H(1,1), Wald tests typically have the best size, but the standard Lagr ange multiplier statistic is badly oversized; versions that are robust to possible nonnormality of the data perform marginally better. An em pirical example demonstrates these results.