MAXIMUM LIKELIHOOD ESTIMATION FOR α-STABLE AUTOREGRESSIVE PROCESSES

• 成果类型: Article
• 署名作者: Andrews, Beth; Calder, Matthew; Davis, Richard A.
• 署名单位: Northwestern University; Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS632
• 发表日期: 2009
• 页码: 1946-1982
• 关键词: absolute deviation estimation; infinite variance; random-variables; Moving averages; limit theory; models

摘要

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian alpha-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are n(1/alpha)-consistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general Conditions. The estimators for the parameters of the stable noise distribution have the traditional n(1/2) rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of Wal-Mart stock traded daily on the New York Stock Exchange.