Estimating Parameters in Autoregressive Models with Asymmetric Innovations

Tiku et al (1999) considered the estimation in a regression model with autocorrelated error in which the underlying distribution be a shift-scaled Student’s t distribution, developed the modified maximum likelihood (MML) estimators of the parameters and showed that the proposed estimators had closed forms and were remarkably efficient and robust. In this paper, we extend the results to the case, where the underlying distribution is a generalized logistic distribution. The generalized logistic distribution family represents very wide skew distributions ranging from highly right skewed to highly left skewed. Analogously, we develop the MML estimators since the ML (maximum likelihood) estimators are intractable for the generalized logistic data. We then study the asymptotic properties of the proposed estimators and conduct simulation to the study.