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Consistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models
IGARCH(1,1)与协方差平稳GARCH(1,1)模型中准极大似然估计的一致性与渐近正态性
This paper provides a proof of the consistency and asymptotic normality of the quasi-maximum likelihood estimator in GARCH(1,1) and IGARCH(1,1) models. In contrast to the case of a unit root in the conditional mean, the presence of a 'unit root' in the conditional variance does not affect the limiting distribution of the estimators; in both models, estimators are normally distributed. In addition, a consistent estimator of the covariance matrix is available, enabling the use…
Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation
GARCH(1,1) 与 IGARCH(1,1) 最大似然估计量的有限样本性质：蒙特卡洛考察
This paper 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. While 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 while the…