Empirical likelihood for LAD estimators in infinite variance ARMA models

In this paper, we use an empirical likelihood method to construct confidence regions for the stationary ARMA(p,q)ARMA(p,q) models with infinite variance. An empirical log-likelihood ratio is derived by the estimating equation of the self-weighted LAD estimator. It is proved that the proposed statistic has an asymptotic standard chi-squared distribution. Simulation studies show that in a small sample case, the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy.