Estimation of FARIMA Parameters in the Case of Negative Memory and Stable Noise

In this paper, we extend a method of estimation of parameters of the fractional autoregressive integrated moving average (FARIMA) process with stable noise to the case of negative memory parameter d. We construct an estimator that is a modification of that of Kokoszka and Taqqu and prove its consistency for -1/2 <; d <; 0. We show that the estimator is accurate and possesses a low variance for FARIMA time series with both light- and heavy-tailed noises. It is illustrated by means of Monte Carlo simulations. Finally, we compare the introduced method of estimation of d with classical methods like the R/S, modified R/S and variance. The results show that the proposed estimator is vastly superior to them.