Recursive estimation of a drifted autoregressive parameter
成果类型：
Article
署名作者：
Belitser, E
署名单位：
Leiden University - Excl LUMC; Leiden University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1015952001
发表日期：
2000
页码：
860-870
关键词：
摘要：
Suppose the X-0, ..., X-n are observations of a one-dimensional stochastic dynamic process described by autoregression equations when the autoregressive parameter is drifted with time, i.e. it is some function of time: theta (0), ..., theta (n), with theta (k) = theta (k/n). The function theta (t) is assumed to belong a priori to a predetermined nonparametric class of functions satisfying the Lipschitz smoothness condition. At each time point t those observations are accessible which have been obtained during the preceding time interval. A recursive algorithm is proposed to estimate theta (t). Under some conditions on the model, we derive the rate of convergence of the proposed estimator when the frequency of observations n tends to infinity.