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Fractional and Seasonal Filtering L. Ferrara ∗and D. Guégan † Abstract We introduce in this study a new strategy to model simultaneously per- sistence and seasonality inside economic data using different stochastic filters based on the Gegenbauer modelling. The limits and advantages of these filters are discussed in order to improve the adjustment of eco- nomic series, particularly when specific trend is observed. The series of new cars registrations in the Euro-zone is modelled using the previous filters. Keywords : Persistence - Seasonality - Fractional filter - Euro-zone new car registrations. JEL classification: C22, C52 ∗Banque de France, DGEI-DAMEP and CES Université Paris 1 Panthéon-Sorbonne, e-mail : ferrara@ces.ens-cachan.fr †PSE, MSE - CES, Université Paris 1 Panthéon-Sorbonne, 106 boulevard de l’hopital, 75013 Paris, e-mail : dominique.guegan@univ-paris1.fr 1 1 Introduction Many economic time series display seasonal fluctuations inherent to the eco- nomic activity. Therefore, models allowing to describe the seasonal compo- nents of the data are essential to accurately analyse and forecast business quantities. During a long time, in economic time series, the seasonal and cyclical movements have been described extending short memory processes, including seasonal components in the models, like with the classical SARIMA (Seasonal Autoregressive Integrated Moving Average) model for instance, see Box and Jenkins (1976). Those models have the specificity to exhibit peaks at seasonal frequencies in the spectral density. Now, several kinds of processes have been proposed in the literature to take simultaneously long range depen- dence and seasonality (see for instance Arteche and Robinson, 2000). They