Fractional seasonality : Models and applications to economic activity in the Euro area, Eurostat Working Paper, presented at the Conference for Seasonality, Seasonal Adjustement and their implications for ShortTerm Analysis and Forecasting, organized by E

Many time series reflecting the economic activity are affected by a strong seasonal behavior as well as by long-range dependence characterized, in the spectral domain, by peaks at the seasonal frequencies. In recent years, frac-tionally integrated seasonal models have been proposed in the statistical liter-ature to take those stylized facts into account, see for instance Porter-Hudak (1990) or Hassler (1994). Generalized long memory models introduced by Gray, Zhang and Woodward (1989, 1994), based on Gegenbauer polynomi-als, have been proved to be an attractive alternative to such models when dealing with real data (see Ferrara and Guégan, 2001a, 2001b). In this paper, we recall some concepts on seasonal long memory, we review the diverse frac-tionally integrated seasonal time series models and we discuss their statistical properties. Then, we compare the empirical performances of those models on euro area economic data and we show that generalized long memory models offer competitive alternatives to classical SARIMA models, avoiding over-differentiation and providing a better goodness of fit. Keywords: Fractional seasonality, long-range dependence, generalized long memory mod-els, economic activity. ∗Paper presented at the Conference for Seasonality, Seasonal Adjustement and thei