FRACTIONALLY DIFFERENCED ARIMA MODELS APPLIED TO HYDROLOGIC TIME-SERIES - IDENTIFICATION, ESTIMATION, AND SIMULATION

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