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.