Bartlett Correctability of Empirical Likelihood for Time Series

Abstract

A desirable feature of the empirical likelihood (EL) method is its Bartlett correctability. Previous studies have only demonstrated that the Bartlett correctability of EL for independent cases. This paper considers the Bartlett correctability of EL in time series models. The validity of the formal Edgeworth expansion for the EL ratio statistic in the short-memory case is established and through meticulous calculations, a closed form expansion for the statistic is deduced. The order of the coverage error of the EL confidence region for time series is obtained based on such an Edgeworth expansion of the EL ratio statistic. It is further demonstrated that the coverage error can be reduced by an order of magnitude after using a Bartlett correction. Finally, a simulation study is presented to illustrate the Bartlett correctability of EL in the short-memory case.