Generalized long memory processes: estimation, prediction and applications.

Summary We are interested in a certain class of parametric time series models: generalized long memory processes, introduced in the statistical literature in the early 1990s. These generalized long memory processes take into account simultaneously in the modeling of the series, a long term dependence and a persistent periodic cyclic component. This type of phenomenon is frequent in many fields of application of statistics, such as economics, finance, environment or public transport. We have proposed a simultaneous pseudo-maximum likelihood estimation method for all the parameters of the model, and a semiparametric method for estimating the long memory parameters. We have shown the consistency of each of these estimators and we have given their limiting distribution, the results being validated by Monte Carlo simulations. We also compared the performance of each of these estimators on real data. For the prediction, we have provided the analytical expressions of the least squares predictor and its confidence interval. We have compared on real data the forecasting performance of generalized long memory processes and other short and long memory processes.