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Valid Edgeworth Expansions of Some Estimators and Bootstrap Confidence Intervals in First‐order Autoregression
Author(s) -
Kakizawa Yoshihide
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00141
Subject(s) - mathematics , autoregressive model , edgeworth series , estimator , studentized range , asymptotic distribution , econometrics , statistics , gaussian , confidence interval , standard error , physics , quantum mechanics
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.