We present a model for hourly electricity load forecasting based on stochastically time-varying processes that are designed to account for changes in customer behaviour and in utility production efficiencies. The model is periodic: it consists of different equations and different parameters for each hour of the day. Dependence between the equations is introduced by covariances between disturbances that drive the time-varying processes. The equations are estimated simultaneously. Our model consists of components that represent trends, seasons at different levels (yearly, weekly, daily, special days and holidays), short-term dynamics and weather regression effects, including nonlinear functions for heating effects. The implementation of our forecasting procedure relies on the multivariate linear Gaussian state space framework, and is applied to the national French hourly electricity load. The analysis focuses on two hours, 9 AM and 12 PM, but forecasting results are presented for all twenty-four hours. Given the time series length of nine years of hourly observations, many features of our model can be estimated readily, including yearly patterns and their time-varying nature. The empirical analysis involves an out-of-sample forecasting assessment up to seven days ahead. The one-day ahead forecasts from forty-eight bivariate models are compared with twenty-four univariate models, one for each hour of the day. We find that the implied forecasting function depends strongly on the hour of the day.
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