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Cressie–Read Power‐Divergence Statistics for Non‐Gaussian Vector Stationary Processes

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  • HIROAKI OGATA
  • MASANOBU TANIGUCHI

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.

Suggested Citation

  • Hiroaki Ogata & Masanobu Taniguchi, 2009. "Cressie–Read Power‐Divergence Statistics for Non‐Gaussian Vector Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 141-156, March.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:1:p:141-156
    DOI: 10.1111/j.1467-9469.2008.00618.x
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    References listed on IDEAS

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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
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    Cited by:

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    2. Yoshihide Kakizawa, 2013. "Frequency domain generalized empirical likelihood method," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 691-716, November.

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