Time series AR(1) model for short-tailed distributions

Abstract

The innovations in AR(1) models in time series have primarily been assumed to have a normal or long-tailed distributions. We consider short-tailed distributions (kurtosis less than 3) and derive modified maximum likelihood (MML) estimators. We show that the MML estimator of φ is considerably more efficient than the commonly used least squares estimator and is also robust. This paper is essentially the first to achieve robustness to inliers and to various forms of short-tailedness in time series analysis.