An empirical likelihood approach for non-gaussian vector stationary processes and its application to minimum contrast estimation

Hiroaki Ogata, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    We develop the empirical likelihood approach for a class of vector-valued, not necessarily Gaussian, stationary processes with unknown parameters. In time series analysis, it is known that the Whittle likelihood is one of the most fundamental tools with which to obtain a good estimator of unknown parameters, and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we apply the empirical likelihood approach to its derivative with respect to unknown parameters. We also consider the empirical likelihood approach to minimum contrast estimation based on a spectral disparity measure, and apply the approach to the derivative of the spectral disparity.This paper provides rigorous proofs on the convergence of our two empirical likelihood ratio statistics to sums of gamma distributions. Because the fitted spectral model may be different from the true spectral structure, the results enable us to construct confidence regions for various important time series parameters without assuming specified spectral structures and the Gaussianity of the process.

    Original languageEnglish
    Pages (from-to)451-468
    Number of pages18
    JournalAustralian and New Zealand Journal of Statistics
    Volume52
    Issue number4
    DOIs
    Publication statusPublished - 2010 Dec

    Fingerprint

    Empirical Likelihood
    Stationary Process
    Whittle Likelihood
    Unknown Parameters
    Stationary Gaussian Process
    Derivative
    Score Function
    Likelihood Ratio Statistic
    Spectral Measure
    Confidence Region
    Time Series Analysis
    Gamma distribution
    Time series
    Estimator
    Stationary process
    Empirical likelihood
    Derivatives
    Model

    Keywords

    • Empirical likelihood
    • Estimating function
    • Minimum contrast estimation
    • Spectral density matrix
    • Whittle likelihood

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

    Cite this

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    abstract = "We develop the empirical likelihood approach for a class of vector-valued, not necessarily Gaussian, stationary processes with unknown parameters. In time series analysis, it is known that the Whittle likelihood is one of the most fundamental tools with which to obtain a good estimator of unknown parameters, and that the score functions are asymptotically normal. Motivated by the Whittle likelihood, we apply the empirical likelihood approach to its derivative with respect to unknown parameters. We also consider the empirical likelihood approach to minimum contrast estimation based on a spectral disparity measure, and apply the approach to the derivative of the spectral disparity.This paper provides rigorous proofs on the convergence of our two empirical likelihood ratio statistics to sums of gamma distributions. Because the fitted spectral model may be different from the true spectral structure, the results enable us to construct confidence regions for various important time series parameters without assuming specified spectral structures and the Gaussianity of the process.",
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    AU - Ogata, Hiroaki

    AU - Taniguchi, Masanobu

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    KW - Estimating function

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    KW - Spectral density matrix

    KW - Whittle likelihood

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