Functional Time Series

Electricity load experts naturally look at daily demand data as time functions called load curves, even when only few discrete records are available at each day (e.g., 24, 48, or 96 point measurements for hourly, half-hourly, or quart hourly sampled load curves, respectively). The shape of the curves contains rich information about the calendar day type, the meteorological conditions, or the existence of special electricity tariffs. We explore in this chapter tools to exploit the information contained in the shape of the load curves and thus the functional structure of the data. In this chapter we first formalize the construction of a functional time series (FTS). Then, we introduce wavelets as an alternative to the spline basis for representing functions. A predictor called KWF is proposed by means of nonparametric regression. While useful for stationary FTS, adaptations need to be introduced to use it on nonstationary signals as the electrical demand. We end the chapter with two clustering strategies that may unveil interesting electrical consumption structures. For this, we exploit the information carried by the shapes of the electrical load curves.