This paper explores seasonal and long-memory time series properties by using the fractional ARIMA model when the data have one and two seasonal periods and short-memory components. The stationarity and invertibility parameter conditions are established for the model studied. To estimate the...

There has recently been great interest in time series with long memory, namely series whose dependence decays slowly in the sense that autocovariances are not summable and the spectral density is unbounded. This concept has been extended to SCLM (Seasonal/Cyclical Long Memory) where the...

Strong cyclical persistence is a common phenomenon that has been documented not only in the levels but also in the volatility of many time series, specially in astronomical or business cycle data. The class of doubly fractional models is extended to include the possibility of long memory in...