Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation
通过蒙特卡洛模拟，比较GARCH(1,1)和IGARCH(1,1)模型中最大似然估计的有限样本表现，发现t统计量近似良好，但其他常用统计量在小样本中表现不佳，且估计量存在偏斜。
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.