Asymptotic Expansions of MM-type and QML Estimators for the MA(1) with Mean Models

Abstract

Listen

Translate article

The second order asymptotic expansions, of the Edgeworth type, of an MM-type and the QML estimators for the MA(1) with mean model are given. We also derive the second order expansions of the sample autocorrelation and the autocorrelation based on the QML estimator of the MA parameter. By employing Nagar type expansions, we compare the estimators in terms of bias and mean squared error. The results presented here are important for deciding on the estimation method we choose, as well as for bias reduction and increasing the efficiency of the estimators. The theoretical results are generally confirmed by a Monte-Carlo exercise.