Improved extreme learning machine for multivariate time series online sequential prediction

Multivariate time series has attracted increasing attention due to its rich dynamic information of the underlying systems. This paper presents an improved extreme learning machine for online sequential prediction of multivariate time series. The multivariate time series is first phase-space reconstructed to form the input and output samples. Extreme learning machine, which has simple structure and good performance, is used as prediction model. On the basis of the specific network function of extreme learning machine, an improved Levenberg–Marquardt algorithm, in which Hessian matrix and gradient vector are calculated iteratively, is developed to implement online sequential prediction. Finally, simulation results of artificial and real-world multivariate time series are provided to substantiate the effectiveness of the proposed method.