On the consistency of the MLE for Ornstein–Uhlenbeck and other selfdecomposable processes

被引：1
作者：
Grabchak M. [1 ]
机构：
[1] Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, 28223, NC
来源：
Statistical Inference for Stochastic Processes | 2016年 / 19卷 / 1期
关键词：
Consistent estimator; MLE; Ornstein–Uhlenbeck processes; Selfdecomposable distributions; Stable distributions; Tempered stable distributions;
D O I：
10.1007/s11203-015-9118-9
中图分类号：
学科分类号：
摘要：
In this paper we give easy to verify conditions for the strong consistency of the maximum likelihood estimator (MLE) in the case when data is sampled from a parametric family of selfdecomposable distributions. The difficulty arises from the fact that standard conditions for the consistency of the MLE are based on the pdf, which, for most selfdecomposable distributions, is not available in a closed form. Instead, our conditions are based on properties of the Lévy triplet (i.e. the Lévy measure, the Gaussian part, and the shift) of the distribution. Further, we extend out results to certain selfdecomposable stochastic processes, and, in particular, we give conditions in the case when the data is sampled from a Lévy or an Ornstein–Uhlenbeck process. © 2015, Springer Science+Business Media Dordrecht.
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页码：29 / 50
页数：21
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