Multivariate time series forecasting method based on nonlinear spiking neural P systems and non-subsampled shearlet transform

Abstract

Multivariate time series forecasting remains a challenging task because of its nonlinear, non-stationary, high-dimensional, and spatial–temporal characteristics, along with the dependence between variables. To address this limitation, we propose a novel method for multivariate time series forecasting based on nonlinear spiking neural P (NSNP) systems and non-subsampled shearlet transform (NSST). A multivariate time series is first converted into the NSST domain, and then NSNP systems are automatically constructed, trained, and predicted in the NSST domain. Because NSNP systems are used as nonlinear prediction models and work in the NSST domain, the proposed prediction method is essentially a multiscale transform (MST)–based prediction method. Therefore, the proposed prediction method can process nonlinear and non-stationary time series, and the dependence between variables can be characterized by the multiresolution features of the NSST transform. Five real-life multivariate time series were used to compare the proposed prediction method with five state-of-the-art and 28 baseline prediction methods. The comparison results demonstrate the effectiveness of the proposed method for multivariate time-series forecasting.