# Quantile deep learning models for multi-step ahead time series prediction

arXiv: https://arxiv.org/abs/2411.15674 · HTML: https://mlsanity.com/paper/2411.15674/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 98 references that are in the map.
- First posted on arXiv 24 Nov 2024.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Sentiment Analysis in the Era of Large Language Models: A Reality Check](https://mlsanity.com/paper/2305.15005/) (2023)
- [Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning](https://mlsanity.com/paper/1902.03932/) (2019)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [Dropout Training as Adaptive Regularization](https://mlsanity.com/paper/1307.1493/) (2013)
- [A review of predictive uncertainty estimation with machine learning](https://mlsanity.com/paper/2209.08307/) (2022)
- [Evaluation of deep learning models for multi-step ahead time series prediction](https://mlsanity.com/paper/2103.14250/) (2021)
- [Gradient boosting for extreme quantile regression](https://mlsanity.com/paper/2103.00808/) (2021)
- [Lecture notes on ridge regression](https://mlsanity.com/paper/1509.09169/) (2015)
- [Inferring Parameters and Structure of Latent Variable Models by Variational Bayes](https://mlsanity.com/paper/1301.6676/) (2013)
- [A horse racing between the block maxima method and the peak-over-threshold approach](https://mlsanity.com/paper/1807.00282/) (2018)
- [Ensemble learning for uncertainty estimation with application to the correction of satellite precipitation products](https://mlsanity.com/paper/2403.10567/) (2024)
- [Review of deep learning models for crypto price prediction: implementation and evaluation](https://mlsanity.com/paper/2405.11431/) (2024)

## Built on by (most cited first, 1 of 1)

- [QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification](https://mlsanity.com/paper/2510.05453/) (2025)

## Abstract (arXiv)

Uncertainty quantification is crucial in time series prediction, and quantile regression offers a valuable mechanism for uncertainty quantification which is useful for extreme value forecasting. Although deep learning models have been prominent in multi-step ahead prediction, the development and evaluation of quantile deep learning models have been limited. We present a novel quantile regression deep learning framework for multi-step time series prediction. In this way, we elevate the capabilities of deep learning models by incorporating quantile regression, thus providing a more nuanced understanding of predictive values. We provide an implementation of prominent deep learning models for multi-step ahead time series prediction and evaluate their performance under high volatility and extreme conditions. We include multivariate and univariate modelling, strategies and provide a comparison with conventional deep learning models from the literature. Our models are tested on two cryptocurrencies: Bitcoin and Ethereum, using daily close-price data and selected benchmark time series datasets. The results show that integrating a quantile loss function with deep learning provides additional predictions for selected quantiles without a loss in the prediction accuracy when compared to the literature. Our quantile model has the ability to handle volatility more effectively and provides additional information for decision-making and uncertainty quantification through the use of quantiles when compared to conventional deep learning models.