The long-term memory prediction by multiscale decomposition

Abstract This paper deals with the problem of long-term memory time-seri es prediction. Traditionally, this type of prediction is achieved using the fractionally integrated ARMA models. The method presented here, is based on the multiscale filtering which iteratively decomposes a series into a trend and a hierarchy of details that are stationary and contain only short memory. Thus, the obtained series are modeled with classical ARMA models. The advantage of this method is that it overcomes the tricky problem of the fractional integration parameter estimation. The statistical properties of the obtained series are studied and the use of multichannel autoregressive models is justified when the moving average part does not exist. Results obtained through the use of both simulated and real-life series show the efficiency of the approach.