Parameter estimation for infinite variance fractional ARIMA

Abstract

Consider the fractional ARIMA time series with innovations that have infinite variance. This is a finite parameter model which exhibits both long-range dependence (long memory) and high variability. We prove the consistency of an estimator of the unknown parameters which is based on the periodogram and derive its asymptotic distribution. This shows that the results of Mikosch, Gadrich, Klüppelberg and Adler for ARMA time series remain valid for fractional ARIMA with long-range dependence. We also extend the limit theorem for sample autocovariances of infinite variance moving averages developed in Davis and Resnick to moving averages whose coefficients are not absolutely summable.