DEVELOPPEMENTS RECENTS DANS LA MODELISATION DE LA PERSISTANCE A LONG TERME

In order to model effectively persistence in hydrologic time series, recent developments in fractional autoregressive-moving average (FARMA) models are presented. A time series possesses persistance or long memory if it has an autocorrelation structure that attenuates slowly to zero with increasing lags. Based on the controversy surrounding the Hurst phenomenon, some hydrologists claim that it is important to employ stochastic models which have the ability to model long memory when it is present in a given time series. Fractional Gaussian noise models and approximations thereof were developed within the field of hydrology in order to be able to model long memory. However, a particularly flexible set of models having the capability to describe long memory is the FARMA family of models, which constitutes a direct generalization of autoregressive integrated moving average (ARIMA) models.