A proposal for measuring and comparing seasonal variations in hourly economic time series

Abstract

Hourly data usually exhibit complex seasonal variations characterized by yearly, monthly, weekly or daily seasonal patterns. Each seasonal variation is modelled by using an evolving spline function 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. Subsequently, the areas under the splines are proposed as a useful tool to measure the changes in the magnitude of seasonal variations over time, and to compare the relevance of seasonal variations with different seasonal periods. Furthermore, two indexes are suggested to compare seasonal variations with the same seasonal period in different time series: a dissimilarity index accounts for the area between the splines corresponding to the seasonal variation for each series, whereas a complementarity index accounts for this area when seasonal effects have opposite signs. The proposal is illustrated by applying it to hourly series of energy demand in Canary Islands.