高阶矩缺失下GARCH模型的M-估计
M-estimation in GARCH Models in the Absence of Higher-Order Moments
摘要：
本文考虑了Gestival（p，q）模型参数的一类M-估计。这些估计涉及得分函数，并为适当的选择的得分函数，渐近正常下温和的时刻假设比通常的准极大似然，这使得他们更可靠的存在重尾。我们还考虑这些M-估计的分布的加权自助逼近，并建立其有效性。通过大量的模拟，我们证明了这些M-估计重尾下的鲁棒性，并进行了比较研究的性能（偏差和均方误差）的各种得分函数和准确性（置信区间覆盖率）的自举近似。除了GARCH（1，1）模型外，我们的模拟还涉及了更高阶的GARCH~（2，1）和GARCH~（1，1）模型。2)到目前为止在文献中得到的关注相对较少。我们还考虑了订单错误指定模型的情况。最后，我们使用我们的M-估计的分析两个实际的金融时间序列拟合的GARCH（1，1）或GARCH（2，1）模型。
英文摘要：
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.
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