Complex-Valued Ordinary Differential Equation Modeling for Time Series Identification

Time series identification is one of the key approaches to dealing with time series data and discovering the change rules. Therefore, time series forecasting can be treated as one of the most challenging issues in this field. In order to improve the forecasting performance, we propose a novel time series prediction model based on a complex-valued ordinary differential equation (CVODE) to predict time series. A multi expression programming (MEP) algorithm is utilized to optimize the structure of the CVODE model. So as to achieve the optimal complex-valued coefficients, a novel optimization algorithm based on a complex-valued crow search algorithm (CVCSA) is proposed. The chaotic Mackey-Glass time series, small-time scale traffic measurements, Nasdaq-100 index, and Shanghai stock exchange composite index are utilized to evaluate the performance of our method. The results prove that our proposed method could predict more accurately than state-of-the-art real-valued neural networks and an ordinary differential equation (ODE). The CVCSA has faster convergence speed and stronger optimization ability than the crow search algorithm (CSA) and particle swarm optimization (PSO).