Probabilistic Forecasting of Electricity Load with Inhomogeneous Markov Switching Models

In this paper we suggest a novel inhomogeneous Markov switching approach for probabilistic forecasting of electricity load of industrial companies, for which the load switches at random times between a production and a standby regime. The model we propose describes the transitions between the regimes by a hidden Markov chain with time-varying transition probabilities depending on calendar variables. The demand during the production regime is modeled by an ARMA process with seasonal patterns, whereas we use a much simpler model for the standby regime to reduce complexity. The maximum likelihood estimation of the parameters is implemented with a Differential Evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness of fit of our model for probabilistic forecasting it is shown that this model often outperforms classical additive time series models as well as homogeneous Markov switching models.We also propose a simple procedure to classify load profiles into ones with and without regime-switching behavior