Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Since Hurst [1951] detected the presence of long-term persistence in hydrologic data, new estimation methods and long-memory models have been developed. The lack of flexibility in representing the combined effect of short and long memory has been the major limitation of stochastic models used to analyze hydrologic time series. In the present paper a fractionally differenced autoregressive integrated moving average (FARIMA) model is considered. In contrast to using traditional ARIMA models, this approach allows the modeling of both short- and long-term persistence in a time series. A framework for identification and estimation is presented. The data do not have to be Gaussian. The resulting model, which replicates the sample probability density of the data, can be used for the generation of long synthetic series. An application to the monthly and daily inflows of Lake Maggiore, Italy, is presented.