Hidden multi-resolution ARMA models for nonlinear time series forecast
非线性时间序列预报的隐多分辨ARMA模型

A class of hidden multi-resolution autoregressive moving average (ARMA) model is studied for forecasting nonlinear time series. The model has ARMA model as the original fine level model, that is, the building blocks. The precision of the model for approximating the true one is determined by the variance among the levels. The autocorrelation functions (ACF) structure of the new model is then studied. The estimation of parameters is easily performed via Bayes method and Metropolis-Hasting algorithm. Furthermore, a new method for nonlinear time series forecast is proposed. The method can be directly applied to hidden multi-resolution model with different building blocks, and reduce the forecasting error compared with other linear method and hidden multi-resolution model forecast method. Finally, the model and approaches are illustrated through the use of both simulated and real series. The new model and forecasting method appear to capture features of the data better and provide more precise forecasting than other competing models do.