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A seasonal fractional autoregressive integrated moving average (ARIMA) model is introduced, with both short‐ and long‐term persistent periodic components. The estimation of the parameters is carried out by applying the Whittle's approximation to the Gaussian maximum likelihood function, which yields asymptotically consistent estimates. This method is particularly useful for hydrological time series. It is applied here to the Nile River monthly flows at Aswan in order to detect whether long memory is present. The results are compared with ones obtained by applying heuristic procedures, some of which were developed recently, in order to see how these perform on seasonal data.
Montanari et al. (Mon,) studied this question.