Adjusted empirical likelihood for long-memory time-series models

Abstract

The empirical likelihood method has been applied to short-memory time-series models by Monti through the Whittle’s estimation method. Yau extended this idea to long-memory time series models. Nordman and Lahiri showed a new formulation of empirical likelihood for inference of dependent data. Asymptotic distributions of the empirical likelihood ratio statistic for short and long-memory time series have been derived to construct confidence regions for the corresponding model parameters. However, computing profile empirical likelihood function involving constrained maximization does not always have a solution, which leads to several drawbacks. In this article, we propose an adjusted empirical likelihood procedure to modify the one proposed by Yau for the autoregressive fractionally integrated moving average (ARFIMA) model. It guarantees the existence of a solution to the required maximization problem and maintains an asymptotic chi-squared distribution. Simulations have been carried out to illustrate that the adjusted empirical likelihood method for different long-time series models provides competitive confidence regions and coverage probabilities compared to the unadjusted ones, especially for small sample sizes.