Chapter 12 Multiple frequencies in ADAM ETS
When we work with weekly, monthly or quarterly data, we do not have more than one seasonal cycle. This is obvious, because one and the same pattern will repeat itself only once a year. For example, we might see an increase in sales of ski equipment over winter, thus the seasonal component for December will by typically higher than the same component in August. However, when we move to the data with higher granularity, we might see several seasonal patterns. For example, daily sales of product will not only have time of year seasonal pattern, but also the day of week one. If we move to hourly data, then the number of seasonal elements might increase to three: hour of day, day of week and time of year. From the modelling point of view, these seasonal patterns should be called either “periodicities” or “frequencies” as the hour of day cannot be considered as a proper “season.”
In order to capture such complicated structure in the data correctly, we need to have a model that includes these multiple frequencies in it. In this chapter, we discuss how this can be done in ADAM framework for both ETS and ARIMA. In addition, when we move to modelling high granularity data, there appear several fundamental issues related to how calendar works and how human beings make their lives more complicated by introducing time changes over the year. Finally, we move to the discussion of a simpler approach, relying on the explanatory variables (discussed in Chapter 10).