  Maximum likelihood methods, while widely used, may be non-robust due to
disagreement between the assumptions upon which the models are based and the
true density probability distribution of observed data. Because the Empirical
Characteristic Function (ECF) is the Fourier transform of the empirical
distribution function, it retains all the information in the sample but can
overcome difficulties arising from the likelihood. This paper discusses an
estimation method via the ECF for stable seasonal fractional ARIMA processes.
Under some assumptions, we show that the resulting estimators are consistent
and asymptotically normally distributed. For comparison purpose, we consider
also the MCMC Whittle method developed by Ndongo et al. (2010). The performance
of the two methods is discussed using a Monte Carlo simulation.
