Estimation of AR(1) Model Having Generalized Logistic Disturbances

Abstract

Non-normality is becoming a common feature in real life applications. Using non-normal disturbances in autoregressive models induces non-linearity in the likelihood equations so that maximum likelihood estimators cannot be derived analytically. Thus, modified maximum likelihood estimation (MMLE) technique is introduced in literature to overcome this difficulty. However, this method assumes the shape parameter to be known which is not realistic in real life. Recently, for unknown shape parameter case, adaptive modified maximum likelihood estimation (AMMLE) method that combines MMLE with Huber estimation method is suggested in literature. In this study, we adopt AMMLE method to AR(1) model where the disturbances are Generalized Logistic distributed. Although Huber M-estimation is not applicable to skew distributions, the AMMLE method extends Huber type work to skew distributions. We derive the estimators and evaluate their performance in terms of effici