Online Sequential Model for Multivariate Time Series Prediction With Adaptive Forgetting Factor

In the process of online prediction of multivariable non-stationary time series by kernel extreme learning machine (KELM), the dynamic characteristics of the system which are difficult to determine have always posed a big problem. We propose an online sequential prediction model with an adaptive forgetting factor (AFF) for multivariable time series to solve this problem. The multivariable time series instead of variable itself is reconstructed firstly. AFF is introduced into the objective function and can be adjusted iteratively and adaptively with the system changes. As a result, higher weight can be allocated for the fresh and more important samples while the old failure samples can be quickly forgotten. The model sparsification uses a fast leave-one-out cross-validation (FLOO-CV) method to set a prediction error threshold so that samples can be selected conditionally to form a dictionary. Besides, the dictionary parameters, including AFF and kernel parameters, are recursively updated simultaneously without increasing calculation complexity. The experimental results show that, compared with four fashionable KLEM methods, the proposed AFF-OSKELM has a better dynamic tracking ability and adaptability. Moreover, compared with single variable prediction, the spatial reconstructed multivariable has higher prediction accuracy and stability.