An improved Elman neural network with piecewise weighted gradient for time series prediction

Abstract

Time series prediction is an important tool for system analysis. Traditional forecasting methods usually achieve prediction by establishing static model or only mining the information from the sequence itself, but without considering the dynamics of the system or its triggering factors. Elman neural network (ENN) is a dynamical model that can remember historical states. In order to better establish the real multivariate time series model and improve the single-step prediction accuracy, this study proposes an improved regularized ENN method based on piecewise time weighted gradient (PWRENN). Each time the parameters of PWRENN model are updated, the weighted gradient is calculated by weighing the current gradient and the previous gradients according to a monotonically increasing temporal function. By considering both the current gradient and previous gradients, PWRENN is able to simulate the time-lag effect in the time series prediction problem. Moreover, the system environment may change with time, and the historical data of the same slot at a different time should have different effects on the predicted data. This work uses a piecewise time function with different parameters at different time periods to more accurately model the real system. In PWRENN, L2 regularization is adopted to solve the overfitting problem and enhance the generalization performance. Furthermore, the effectiveness of the proposed method is verified in an artificial Mackey-Glass time series prediction and three landslide displacement predictions.