Recursive estimation of a drifted autoregressive parameter

E. Belitser

    Research output: Contribution to journalArticleAcademicpeer-review

    8 Citations (Scopus)
    55 Downloads (Pure)

    Abstract

    Suppose the X0,...., Xn 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: ¿0,...., ¿n, with ¿k = ¿ (k/n). The function ¿(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 ¿??t??. Under some conditions on the model, we derive the rate of convergence of the proposed estimator when the frequencyof observations n tends to infinity.
    Original languageEnglish
    Pages (from-to)860-870
    Number of pages11
    JournalThe Annals of Statistics
    Volume28
    Issue number3
    DOIs
    Publication statusPublished - 2000

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