Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation

Abstract

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

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