PARAMETER-ESTIMATION FOR ARMA MODELS WITH INFINITE VARIANCE INNOVATIONS

• 成果类型: Article
• 署名作者: MIKOSCH, T; GADRICH, T; KLUPPELBERG, C; ADLER, RJ
• 署名单位: Technion Israel Institute of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324469
• 发表日期: 1995
• 页码: 305-326
• 关键词: AUTOREGRESSIVE PROCESSES; time-series

摘要

We consider a standard ARMA process of the form phi(B)X(t) = B(B)Z(t), where the innovations Z(t) belong to the domain of attraction of a stable law, so that neither the Z(t) nor the X(t) have a finite variance. Our aim is to estimate the coefficients of phi and theta. Since maximum likelihood estimation is not a viable possibility (due to the unknown form of the marginal density of the innovation sequence), we adopt the so-called Whittle estimator, based on the sample periodogram of the X sequence. Despite the fact that the periodogram does not, a priori, seem like a logical object to study in this non-L(2) situation, we show that our estimators are consistent, obtain their asymptotic distributions and show that they converge to the true values faster than in the usual L(2) case.