CONVERGENCE OF MOMENTS OF LEAST-SQUARES ESTIMATORS FOR THE COEFFICIENTS OF AN AUTOREGRESSIVE PROCESS OF UNKNOWN ORDER

• 成果类型: Article
• 署名作者: BHANSALI, RJ; PAPANGELOU, F
• 署名单位: University of Manchester
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348243
• 发表日期: 1991
• 页码: 1155-1162
• 关键词: time-series; models; derivation; predictors

摘要

Given a realization of T consecutive observations of a stationary autoregressive process of unknown, possibly infinite, order m, it is assumed that a process of arbitrary finite order p is fitted by least squares. Under appropriate conditions it is known that the estimators of the autoregressive coefficients are asymptotically normal. The question considered here is whether the moments of the (scaled) estimators converge, as T --> infinity, to the moments of their asymptotic distribution. We establish a general result for stationary processes (valid, in particular, in the Guassian case) which is sufficient to imply this convergence.