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

• We present a novel quantile regression deep learning framework for multi-step time series prediction. • We elevate the capabilities of deep learning models by incorporating quantile regression. • We include multivariate and univariate modelling strategies and compare with conventional deep learning models. • The model provide additional predictions without a loss in the prediction accuracy when compared to the literature. 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 prediction accuracy. Our quantile model can handle volatility more effectively and provides uncertainty quantification through the use of quantiles when compared to conventional deep learning models.