State-dependent vector hybrid linear and nonlinear ARMA modeling: Applications

In a recent companion paper, a new method has been presented for modeling g eneral vector nonstationary and nonlinear processes based on a state-depend ent vector hybrid linear and nonlinear autoregressive moving average (SVH-A RMA) model. This paper discusses some potential applications of the SVH-ARM A model, including Signal filtering, time series prediction, and system con trol. First, a state-space model governed by a hidden Markov Chain is shown to be equivalent to the SVH-ARMA model. Based on this state-space model, t he extended Kalman filtering and Bayesian estimation techniques are applied for noisy signal enhancement. The result of a noisy image enhancement veri fies that the model can track the time-varying statistical characteristics of nonstationary and nonlinear processes adaptively. Second, the SVH-ARMA m odel is used for a vector time series prediction, which can attain more acc urate multiple step ahead prediction, than conventional forecasting methods . Third, a new technique is developed for predicting scalar long correlatio n time series in the wavelet scale space domain based on the SVH-ARMA model . Dyadic wavelet transform is employed to convert a scalar time series to a vector time series, to which the SVH-ARMA model is applied for vector time series prediction. More accurate and robust forecasting results in both on e step and multiple step ahead prediction can be gained. See also the compa nion paper on theory, by Zheng et al., pp. 551-574, this issue.