Parallel deep prediction with covariance intersection fusion on non-stationary time series

Abstract The prediction of time series can help the advanced estimation and management for scientific decision-making in many fields. The non-stationary trend and complex noises make the time series hard to predict. To utilize the learning ability of the deep neural networks, a novel hybrid prediction method is proposed combining data decomposition and parallel deep network. First, the original time series data are divided into multiple groups with a self-defined method for the following parallel networks. Then, each group of data is decomposed into the period, trend, and residual components for the precise feature extraction. Each component is separately trained with a deep network, and the networks are selected to form the parallel prediction model. Finally, the covariance intersection fusion method is introduced to integrate the multiple results based on the estimation of error level. The proposed method is tested on the meteorological data and air pollutant data in Beijing. The method achieves optimal results than the single deep network and traditional integration method. The parallel deep prediction model with the covariance intersection can extract the time series features more integrally and subtly. And it can effectively predict the non-stationary time series with complex noises.