Multivariate time series prediction by neural network combining SVD

Multivariate time series are common in experimental and real systems. According to the embedding theory, in the absence of observational noise only one time series should be needed to recover dynamics. However, for real data, the noise always exist. There may be large advantages in using more measurements. In this paper, we focus on the issue of using multivariate time series to model and predict. The experiments show that by using multivariate time series the influence of noise could be reduced. Since the structure of the embedded time series is complex, the singular value decomposition (SVD) is used to extract feature components in the multivariate time series. Then the neural network (NN) is applied for identification of the dynamic system. The effectiveness of this method is shown by simulation of the real world multivariate time series as well as a well-known chaotic benchmark system.