Heterogeneous Seasonal Patterns in Agricultural Data and Evolving Splines

In this paper an appropriate model of the seasonal pattern in high frequency agricultural data is proposed that takes the specific nature of such a pattern into account. The methodological proposal is based on evolving splines that are shown to be a tool capable of modelling seasonal variations in which either the period or the magnitude of the seasonal fluctuations do not remain the same over time. The seasonal pattern in each year or agricultural campaign is modelled in such a way that the seasonal effect at each season is a function of the seasonal effects corresponding to some fixed seasons that act as reference points. The spline function is enforced to satisfy several conditions that provide some regularity in the adjusted seasonal fluctuation; on the other hand, the main source of changes in the adjusted seasonal pattern is obtained by assuming that the values of the seasonal effects at the fixed reference seasons do not remain the same year by year. If the length of the period in which the seasonal fluctuation is completed does not change, the proposed specification is flexible enough to test the hypothesis that the seasonal pattern in several consecutive years is fixed by using simple statistical procedures. This proposal is applied to capture the movements in a weekly tomato export series and the analysis is carried out inside the frame delimited by the structural approach to time series