On the Bartlett correction of empirical likelihood for Gaussian long-memory time series

Bartlett correction is one of the desirable features of empirical likelihood (EL) since it allows constructions of confidence regions with improved coverage probabilities. Previous studies demonstrated the Bartlett correction of EL for independent observations and for short-memory time series. By establishing the validity of Edgeworth expansion for the signed root empirical log-likelihood ratio, the validity of Bartlett correction of EL for Gaussian long-memory time series is established. In particular, orders of the coverage error of confidence regions can be reduced from log⁶ n/n to log³ n/n, which is different from the classical rate of reduction from n^-1 to n^-2.