A New Pearson-Type QMLE for Conditionally Heteroscedastic Models
提出一种新型皮尔逊型拟极大似然估计（PQMLE），能同时捕捉GARCH模型中的厚尾和有偏创新，在严格平稳和弱矩条件下得到强一致性和渐近正态性，模拟和实际股票指数、汇率数据验证了其有效性。
This article proposes a novel Pearson-type quasi-maximum likelihood estimator (QMLE) of GARCH(p, q) models. Unlike the existing Gaussian QMLE, Laplacian QMLE, generalized non-Gaussian QMLE, or LAD estimator, our Pearsonian QMLE (PQMLE) captures not just the heavy-tailed but also the skewed innovations. Under strict stationarity and some weak moment conditions, the strong consistency and asymptotic normality of the PQMLE are obtained. With no further efforts, the PQMLE can be applied to other conditionally heteroscedastic models. A simulation study is carried out to assess the performance of the PQMLE. Two applications to four major stock indexes and two exchange rates further highlight the importance of our new method. Heavy-tailed and skewed innovations are often observed together in practice, and the PQMLE now gives us a systematic way to capture these two coexisting features. © 2015 American Statistical Association.