Forecasting with k ‐factor Gegenbauer Processes: Theory and Applications

This paper deals with the k ‐factor extension of the long memory Gegenbauer process proposed by Gray et al . (1989). We give the analytic expression of the prediction function derived from this long memory process and provide the h ‐step‐ahead prediction error when parameters are either known or estimated. We investigate the predictive ability of the k ‐factor Gegenbauer model on real data of urban transport traffic in the Paris area, in comparison with other short‐ and long‐memory models. Copyright © 2001 John Wiley & Sons, Ltd.