Estimating multiple fractional seasonal long-memory parameter

This paper explores seasonal and long-memory time series properties by using the seasonal fractionally ARIMA model when the seasonal data has two seasonal periods, namely, s1 and s2. The stationarity and invertibility parameter conditions are established for the model studied. To estimate the memory parameters, the method given in Reisen, Rodrigues and Palma (2006 a,b), which is a variant of the technique proposed in Geweke and Porter-Hudak (1983) (GPH), is generalized here to deal with a time series with multiple seasonal fractional long-memory parameters. The accuracy of the method is investigated through Monte Carlo experiments and the good performance of the estimator indicates that it can be an alternative procedure to estimate seasonal and cyclical long-memory time series data.