A novel time series probabilistic prediction approach based on the monotone quantile regression neural network.

Quantile regression is widely applied in various fields such as economy, energy, meteorological prediction research in recent years since it does not require distribution assumptions, has relatively loose conditions, and can effectively estimate the uncertainty of time series forecasting. In this paper, a monotone quantile regression neural network (MQRNN) framework is constructed for time series quantile forecasting. The proposed approach takes the monotonicity of quantile into consideration and handles the quantile crossing problem by adding the quantile information into the input structure and using the gradient based point-wise loss function. Aiming at the complex characteristics of time series, such as time-varying and asymmetric heavy-tailed features, a new quantile function is utilized to describe the complete conditional distribution information of data. Under this model framework, non-crossing multiple quantiles can be predicted simultaneously. The proposed approach is implemented based on artificial neural networks, and the constructed model is applied to actual data in different fields. The experimental results demonstrate that the proposed method combined with long short-term memory (LSTM) can provide accurate and reliable multi-quantile prediction, and alleviate the problem of quantile crossing. [ABSTRACT FROM AUTHOR]