Deep distributional time series models and the probabilistic forecasting of intraday electricity prices
提出两种基于回声状态网络的深度概率时间序列模型，用于日内电价预测，在澳大利亚市场数据上验证了其准确性，其中Copula模型表现更优。
Summary 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 Bayesian prior for regularization. The second employs the implicit copula of an ESN with Gaussian disturbances, which is a Gaussian copula process on the feature space. Combining this copula process with a nonparametrically estimated marginal distribution produces a distributional time series model. The resulting probabilistic forecasts are deep functions of the feature vector and marginally calibrated. In both approaches, Markov chain Monte Carlo methods are used to estimate the models and compute forecasts. The proposed models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian market, we show that our deep time series models provide accurate short‐term probabilistic price forecasts, with the copula model dominating. Moreover, the models provide a flexible framework for incorporating probabilistic forecasts of electricity demand, which increases upper tail forecast accuracy from the copula model significantly.