On asymptotic normality of sequential LS-estimate for unstable autoregressive process AR(2)

Leonid Galtchouk, Victor Konev

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    For estimating parameters in an unstable AR(2) model, the paper proposes a sequential least squares estimate with a special stopping time defined by the trace of the observed Fisher information matrix. It is shown that the sequential LSE is asymptotically normally distributed in the stability region and on its boundary in contrast to the usual LSE, having six different types of asymptotic distributions on the boundary depending on the values of the unknown parameters. The asymptotic behavior of the stopping time is studied.

    Original languageEnglish
    Pages (from-to)2616-2636
    Number of pages21
    JournalJournal of Multivariate Analysis
    Volume101
    Issue number10
    DOIs
    Publication statusPublished - Nov 2010

    Keywords

    • Asymptotic normality
    • Autoregressive process
    • Least squares estimate
    • Sequential estimation

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Numerical Analysis
    • Statistics and Probability

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