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Asymptotic Expansions For The Distribution Of An Estimator In The First‐Order Autoregressive Process

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  • Yoshimichi Ochi

Abstract

. In this paper, two asymptotic expansions for the distribution for an estimator of the parameter in a first‐order autoregressive process are derived, according to two situations. Some well known estimators are special cases of the estimator discussed here. The series expansions are carried to terms of order T‐1.

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  • Yoshimichi Ochi, 1983. "Asymptotic Expansions For The Distribution Of An Estimator In The First‐Order Autoregressive Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 57-67, January.
    • Handle: RePEc:bla:jtsera:v:4:y:1983:i:1:p:57-67
    DOI: 10.1111/j.1467-9892.1983.tb00358.x
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    Cited by:

    1. Jorge Arevalillo, 2012. "Exploring the relation between the r* approximation and the Edgeworth expansion," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1009-1024, November.
    2. Marsh, Patrick, 2001. "Edgeworth expansions in Gaussian autoregression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 233-241, October.
    3. Kakizawa, Yoshihide, 1998. "On exponential rates of estimators of the parameter in the first-order autoregressive process," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 355-362, July.
    4. Jorge Arevalillo, 2014. "Higher-order approximations to the quantile of the distribution for a class of statistics in the first-order autoregression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 291-310, June.

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