Seasonality in High Frequency Time Series

Time series observed at higher frequencies than monthly frequency display complex seasonal patterns that result from the combination of multiple seasonal patterns (with annual, monthly, weekly and daily periodicities) and varying periods, due to the irregularity of the calendar. Seasonality in high frequency data is modelled from two main perspectives: the stochastic harmonic approach, based on the Fourier representation of a periodic function, and the time-domain random effects approach. An encompassing representation illustrates the conditions under which they are equivalent. Three major challenges are considered: the first deals with modelling the effect of moving festivals, holidays and other breaks due to the calendar. Secondly, robust estimation and filtering methods are needed to tackle the level of outlier contamination, which is typically high, due to the lower level of temporal aggregation and the raw nature of the data. Finally, model selection strategies play an important role, as the number of harmonic or random components that are needed to account for the complexity of seasonality can be very large.