The Cornish-Fisher expansion for a class of statistics in first order autoregression

ABSTRACT

This article is concerned with the derivation and study of the Cornish-Fisher expansion for a wide class of estimators of the parameter in the first order autoregressive process. Second and third order Cornish-Fisher approximations to the quantile of the distribution of the corresponding asymptotically normal standardized statistic are stated explicitly and their accuracy is examined, both theoretically and numerically, by comparing them with the exact value of the quantile obtained by Monte Carlo simulation.

KEYWORDS:

• Quantile
• Edgeworth expansion
• Cornish-Fisher
• First-order autoregression.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E20
• 62G20
• 62M10