Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method, confidence regions for the stationary AR(p)-ARCH(q) models are constructed. A self-weighted LAD estimator is proposed under weak moment conditions. An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained. Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy, especially for relative small size of observation.