论文标题
在没有高阶力矩的情况下，GARCH模型中的M估计
M-estimation in GARCH Models in the Absence of Higher-Order Moments
论文作者
论文摘要
我们考虑了GARCH（P，Q）的参数的一类M估计器。这些估计量涉及得分函数，并且，对于分数函数的足够选择，在较温和的矩假设下比通常的准准最大可能性渐近地正常，这使得它们在存在重尾巴的情况下更可靠。我们还考虑了这些M估计器的分布的加权自举近似，并确定了它们的有效性。通过大量的模拟，我们证明了这些M测验器在重尾部下的鲁棒性，并对各种得分函数的性能（偏见和平方误差）进行了比较研究以及其引导程序近似值的准确性（置信区间覆盖率）。除了GARCH（1，1）模型外，我们的模拟还涉及高阶模型，例如Garch〜（2，1）和Garch〜（1，〜\！2），到目前为止，这些模型在文献中受到了相对较少的关注。我们还考虑了订单限定模型的情况。最后，我们在分析两个真实的财务时间序列中，使用了Garch（1，1）或Garch（2，1）模型的分析。
We consider a class of M-estimators of the parameters of a GARCH (p,q) model. These estimators involve score functions and, for adequate choices of the score functions, are asymptotically normal under milder moment assumptions than the usual quasi maximum likelihood, which makes them more reliable in the presence of heavy tails. We also consider weighted bootstrap approximations of the distributions of these M-estimators and establish their validity. Through extensive simulations, we demonstrate the robustness of these M-estimators under heavy tails and conduct a comparative study of the performance (bias and mean squared errors) of various score functions and the accuracy (confidence interval coverage rates) of their bootstrap approximations. In addition to the GARCH (1, 1) model, our simulations also involve higher-order models such as GARCH~(2, 1) and GARCH~(1,~\!2) which so far have received relatively little attention in the literature. We also consider the case of order-misspecified models. Finally, we use our M-estimators in the analysis of two real financial time series fitted with GARCH (1, 1) or GARCH (2, 1) models.
