On asymptotic normality of sequential LS-estimates of unstable autoregressive processes

L. Galtchouk, V. Konev

    Research output: Contribution to journalArticle

    Abstract

    For estimating the unknown parameters in an unstable autoregressive AR(p), the article proposes sequential least squares estimates (LSEs) with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting distribution of the sequential LSE is shown to be normal for the parameter vector lying both inside the stability region and on some part of its boundary in contrast to the ordinary LSE. The asymptotic normality of the sequential LSE is provided by a new property of the observed Fisher information matrix that holds both inside the stability region of AR(p) process and on the part of its boundary. The asymptotic distribution of the stopping time is derived. Numerical results for AR(3) processes are given.

    Original languageEnglish
    Pages (from-to)117-144
    Number of pages28
    JournalSequential Analysis
    Volume30
    Issue number2
    DOIs
    Publication statusPublished - 1 Apr 2011

    Fingerprint

    Fisher information matrix
    Least Squares Estimate
    Autoregressive Process
    Asymptotic Normality
    Unstable
    Observed Information
    Fisher Information Matrix
    Stopping Time
    Stability Region
    Estimate
    Ordinary Least Squares
    Limiting Distribution
    Unknown Parameters
    Asymptotic distribution
    Trace
    Numerical Results

    Keywords

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

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation

    Cite this

    On asymptotic normality of sequential LS-estimates of unstable autoregressive processes. / Galtchouk, L.; Konev, V.

    In: Sequential Analysis, Vol. 30, No. 2, 01.04.2011, p. 117-144.

    Research output: Contribution to journalArticle

    Galtchouk, L. ; Konev, V. / On asymptotic normality of sequential LS-estimates of unstable autoregressive processes. In: Sequential Analysis. 2011 ; Vol. 30, No. 2. pp. 117-144.
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