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Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes


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  • Taniguchi, Masanobu
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    In this paper we investigate various third-order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes by the third-order Edgeworth expansions of the sampling distributions. We define a third-order asymptotic efficiency by the highest probability concentration around the true value with respect to the third-order Edgeworth expansion. Then we show that the maximum likelihood estimator is not always third-order asymptotically efficient in the class A3 of third-order asymptotically median unbiased estimators. But, if we confine our discussions to an appropriate class D ([subset of] A3) of estimators, we can show that appropriately modified maximum likelihood estimator is always third-order asymptotically efficient in D.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 18 (1986)
    Issue (Month): 1 (February)
    Pages: 1-31

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    Handle: RePEc:eee:jmvana:v:18:y:1986:i:1:p:1-31

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    Keywords: Gaussian autoregressive moving average processes spectral density Toeplitz matrix maximum likelihood estimator third order asymptotic efficiency Edgeworth expansion residue theorem;


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    Cited by:
    1. Srivastava, V. K. & Maekawa, Koichi, 1995. "Efficiency properties of feasible generalized least squares estimators in SURE models under non-normal disturbances," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 99-121.
    2. Kano, Yutaka, 1998. "More Higher-Order Efficiency: Concentration Probability," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 349-366, November.
    3. Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006. "Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 673-702, August.


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