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

In a recent companion paper, a new method has been presented for modeling general vector nonstationary and nonlinear processes based on a state-dependent vector hybrid linear and nonlinear autoregressive moving average (SVH-ARMA) model. This paper discusses some potential applications of the SVH-ARMA model, including signal filtering, time series prediction, and system control. 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, the extended Kalman filtering and Bayesian estimation techniques are applied for noisy signal enhancement. The result of a noisy image enhancement verifies that the model can track the time-varying statistical characteristics of nonstationary and nonlinear processes adaptively. Second, the SVH-ARMA model is used for a vector time series prediction, which can attain more accurate multiple step ahead prediction, than conventional forecasting methods. Third, a new technique is developed for predicting scalar long correlation 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 one step and multiple step ahead prediction can be gained. See also the companion paper on theory, by Zheng et al., pp. 551–574, this issue.