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

Yoshihide Kakizawa

Journal of Time Series Analysis, 1999, vol. 20, issue 3, 343-359

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.

Date: 1999
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