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

arXiv: https://arxiv.org/abs/2010.01844 · HTML: https://mlsanity.com/paper/2010.01844/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 11 of 11)

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- [M5 Competition Uncertainty: Overdispersion, distributional forecasting, GAMLSS and beyond](https://mlsanity.com/paper/2107.06675/) (2021)
- [Bayesian Hierarchical Probabilistic Forecasting of Intraday Electricity Prices](https://mlsanity.com/paper/2403.05441/) (2024)
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- [Conformal Prediction for Electricity Price Forecasting in the Day-Ahead and Real-Time Balancing Market](https://mlsanity.com/paper/2502.04935/) (2025)
- [Marginally calibrated response distributions for end-to-end learning in autonomous driving](https://mlsanity.com/paper/2110.01050/) (2021)
- [Multivariate Scenario Generation of Day-Ahead Electricity Prices using Normalizing Flows](https://mlsanity.com/paper/2311.14033/) (2023)
- [Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2504.02518/) (2025)
- [Probabilistic intraday electricity price forecasting using generative machine learning](https://mlsanity.com/paper/2506.00044/) (2025)
- [The Evolution of Probabilistic Price Forecasting Techniques: A Review of the Day-Ahead, Intra-Day, and Balancing Markets](https://mlsanity.com/paper/2511.05523/) (2025)
- [PROSWIN: Probabilistic Solar Wind Speed Forecasting Using Deep Distributional Regression From Solar Images](https://mlsanity.com/paper/2609.26683/) (2026)

## Abstract (arXiv)

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 models are suitable for the complex task of forecasting intraday electricity prices. Using data from the Australian National Electricity 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 as additional features, which increases upper tail forecast accuracy from the copula model significantly.