  In this paper we derive the asymptotic properties of the least squares
estimator (LSE) of fractionally integrated autoregressive moving-average
(FARIMA) models under the assumption that the errors are uncorrelated but not
necessarily independent nor martingale differences. We relax considerably the
independence and even the martingale difference assumptions on the innovation
process to extend the range of application of the FARIMA models. We propose a
consistent estimator of the asymptotic covariance matrix of the LSE which may
be very different from that obtained in the standard framework. A
self-normalized approach to confidence interval construction for weak FARIMA
model parameters is also presented. All our results are done under a mixing
assumption on the noise. Finally, some simulation studies and an application to
the daily returns of stock market indices are presented to corroborate our
theoretical work.
