Parameter estimation for moving averages with positive innovations

Abstract

This paper continues the study of time series models generated by nonnegative innovations which was begun by Feigin and Resnick. We concentrate on moving average processes. Estimators for moving average coefficients are proposed and consistency and asymptotic distributions established for the case of an order-one moving average assuming either the right or the left tail of the innovation distribution is regularly varying. The rate of convergence can be superior to that of the Yule-Walker or maximum likelihood estimators.