The Nature of Seasonality in Spanish Tourism Time Series

This paper deals with the analysis of seasonality in the context of tourism time series. The authors present a general testing procedure that permits them to consider the cases of deterministic and/or stochastic (with integer and fractional differentiation) seasonality in a unified treatment. The procedure is applied to four Spanish tourism time series: the total (foreign and domestic) number of tourists, the number of domestic tourists, the number of nights spent in hotel accommodation by tourists, and the number of nights spent in hotel accommodation by domestic tourists. The results show that the series can be well described in terms of seasonally fractionally integrated models, with the orders of integration ranging between 0.4 and 0.6 in the case of white noise disturbances, and values slightly smaller with autocorrelated disturbances. Thus the standard practice of taking seasonal dummies (deterministic seasonality) or integer differentiation (seasonal unit roots) may lead to erroneous conclusions about the stochastic behaviour of the series. Moreover, the series seem to be mean reverting, implying that shocks affecting them disappear in the long run though at a very slow hyperbolic rate.