Bayesian density forecasting of intraday electricity prices using multivariate skew t distributions

Electricity spot prices exhibit strong time series properties, including substantial periodicity, both inter-day and intraday serial correlation, heavy tails and skewness. In this paper we capture these characteristics using a first order vector autoregressive model with exogenous effects and a skew t distributed disturbance. The vector is longitudinal, in that it comprises observations on the spot price at intervals during a day. A band two inverse scale matrix is employed for the disturbance, as well as a sparse autoregressive coefficient matrix. This corresponds to a parsimonious dependency structure that directly relates an observation to the two immediately prior, and the observation at the same time the previous day. We estimate the model using Markov Chain Monte Carlo, which allows for the evaluation of the complete predictive distribution of future spot prices. We apply the model to hourly Australian electricity spot prices observed over a three year period, with four different nested multivariate error distributions: skew t, symmetric t, skew normal and symmetric normal. The forecasting performance is judged over a 30 day forecast trial using the continuous ranked probability score, which accounts for both predictive bias and sharpness.