Splines and the proportion of the seasonal period as a season index

In this paper a seasonal model is proposed to deal with heterogeneous seasonal patterns, in which neither the length of the seasonal period nor the magnitude of the seasonal effects remains the same over time. In these settings, there is a need for parsimony and flexibility. To this end, the seasonal effect at a season is defined as a function of the proportion of the length of the seasonal period elapsed up to this season, and the seasonal pattern is modelled by means of evolving splines. The methodology is illustrated for weekly Canary tomato exports.