Seasonal variations in daily data: An application to air passenger arrivals

The aim of this paper is to describe and compare seasonal effects in daily air passenger arrivals. Multiple seasonal cycles of different lengths are usually observed in daily time series. To model weekly cycles over a short and fixed seasonal period, conventional formulations can be applied. However, the length of yearly and, above all, monthly seasonal cycles is not fixed. Yet, whatever the lengths of the seasonal periods, seasonal cycles can be modelled by using evolving spline functions in such a way that a seasonal effect at a proportion of the seasonal period is defined as a non-fixed parametric formulation of this proportion. Thus, restricted evolving spline models are useful to model this type of seasonal variation. The areas under the splines can measure changes in the magnitude of seasonal variations over time and can be used to compare the relevance of seasonal variations for different seasonal periods or different time series. This proposal is illustrated by applying it to daily series of air passengers arriving in the Canary Islands and at the rest of Spain's airports.