Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices

Recurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a shrinkage prior for additional regularization. The second approach employs the implicit copula of an ESN with Gaussian disturbances, which is a deep copula process on the feature space. Combining this copula with a non-parametrically estimated marginal distribution produces a deep distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and also marginally calibrated. In both approaches, Bayesian Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed deep time series models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian National Electricity Market, we show that our models provide accurate probabilistic price forecasts. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand as additional features. We demonstrate that doing so in the deep distributional time series model in particular, increases price forecast accuracy substantially.