A novel recursive multivariate nonlinear time-series modeling method by using the coupling identification concept

This paper focuses on the modeling problem of complex time -series based on a type of multivariate nonlinear model with colored noise, i.e., the M-RBF-ARMA model. For the purpose of achieving highly accuracy modeling performance under colored noise interference, a novel recursive parameter identification algorithm for the M-RBF-ARMA model is investigated. In the framework of constructing several univariate system and noise sub -identification models using the mixed parameter characteristic of the model, three recursive sub -algorithms are presented by applying the coupling identification concept. Based on the singular value decomposition, a recursive update approach with numerical stability for covariance matrices is given. Then a threestage coupled average extended recursive algorithm is proposed for the M-RBF-ARMA model by using the interactive strategy, which can implement the separable and interactive identification of different type of parameters. The effectiveness of the proposed algorithm is verified by an illustrative and a real multivariate nonlinear time -series.