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.