Modulated cycles, an approach to modelling periodic components from rapidly sampled data

Unobserved components models provide a natural framework for the estimation and forecasting of periodic components embedded in the time series, such as business cycles or seasonality. However, periodic behaviour can be complicated to analyse when dealing with rapidly sampled data of the kind encountered in electricity demand forecast problems. Data of this nature tend to show a multiplicity of superimposed periodic patterns, including annual, weekly and daily cycles. In this paper, we present a new seasonal component model based on modulated periodic components, which is capable of replicating multiplicative periodic components in an efficient manner, in the sense that the number of parameters in the model is much lower than in a standard unobserved components model without modulation. The model performance compares favourably with respect to standard techniques on a rolling forecasting exercise based on actual hourly electricity load demand data at a certain transformer in the UK.