Cressie-read power-divergence statistics for non-gaussian vector stationary processes

Hiroaki Ogata, Masanobu Taniguchi

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    2 Citations (Scopus)

    Abstract

    For a class of vector-valued non-Gaussian stationary processes, we develop the Cressie-Read power-divergence (CR) statistic approach which has been proposed for the i.i.d. case. The CR statistic includes empirical likelihood as a special case. Therefore, by adopting this CR statistic approach, the theory of estimation and testing based on empirical likelihood is greatly extended. We use an extended Whittle likelihood as score function and derive the asymptotic distribution of the CR statistic. We apply this result to estimation of autocorrelation and the AR coefficient, and get narrower confidence intervals than those obtained by existing methods. We also consider the power properties of the test based on asymptotic theory. Under a sequence of contiguous local alternatives, we derive the asymptotic distribution of the CR statistic. The problem of testing autocorrelation is discussed and we introduce some interesting properties of the local power.

    Original languageEnglish
    Pages (from-to)141-156
    Number of pages16
    JournalScandinavian Journal of Statistics
    Volume36
    Issue number1
    DOIs
    Publication statusPublished - 2009 Mar

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    Keywords

    • Empirical likelihood
    • Estimating function
    • Local asymptotic normality
    • Spectral density matrix
    • Whittle likelihood

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

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