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Valid Edgeworth Expansions of Some Estimators and Bootstrap Confidence Intervals in First‐order Autoregression

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  • Yoshihide Kakizawa

Abstract

We derive the third‐order valid Edgeworth expansions for the standardized and the Studentized versions of some estimators in first‐order autoregression without Gaussianity. As a special case of a Gaussian process, the validity of the expansion obtained by Ochi (Asymptotic expansions for the distribution of an estimator in the first‐order autoregressive process. Journal of Time Ser. Anal. 4 (1983), 57–67) is demonstrated. By applying the second‐order Edgeworth expansion to the bootstrap procedure, we construct the confidence intervals for the autoregressive coefficient.

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  • Yoshihide Kakizawa, 1999. "Valid Edgeworth Expansions of Some Estimators and Bootstrap Confidence Intervals in First‐order Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(3), pages 343-359, May.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:3:p:343-359
    DOI: 10.1111/1467-9892.00141
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    1. Marsh, Patrick, 2001. "Edgeworth expansions in Gaussian autoregression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 233-241, October.

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