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

TL;DR

This work presents a novel quantile regression deep learning framework for multi-step time series prediction that 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.

Abstract

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.

Figures (11)

• Figure 1: The uncertainty range provided in the demand forecast using quantile regression includes the forecast mean and the trend of the upper and lower quantiles (25% and 75%).
• Figure 2: Bidirectional-LSTM network showing the flow of information.
• Figure 3: Quantile recurrent neural network for one-step ahead and multi-step ahead prediction using two strategies, i.) grouped percentiles (Panel b) and ii.) vector-based quantiles (Panel c). Note that the vector-based quantiles have further connections to the hidden neurons, which is not explicitly shown. In the case of the multivariate features, additional neurons in the input layer can be added for each feature. The time-based input and recurrent connections are also not explicitly suing in the recurrent neural network. $x$ represents the time series data index by time $t$ that is windowed by size $d$ for $m$ step-ahead prediction.
• Figure 4: Framework diagram showing the key stages that include data processing model  training and evaluation. We present quartile-based implementation for a a set of deep learning models including BD-LSTM, Conv-LSTM, and ED-LSTM.
• Figure 5: Cryptocurrency time series reporting daily close prices