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

L. Galtchouk, V. Konev

    Результат исследования: Материалы для журналаСтатья

    Аннотация

    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.

    Язык оригиналаАнглийский
    Страницы (с... по...)117-144
    Количество страниц28
    ЖурналSequential Analysis
    Том30
    Номер выпуска2
    DOI
    Статус публикацииОпубликовано - 1 апр 2011

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    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation

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