Extraction of Dynamics from Non-stationary Time Series Data

. One of the main mechanisms to generate non-stationary data is that the system's environment is always changing with time. It is appropriate to approximate non-stationary time series using the model: Xn+1 = F (Xn ; Un ); where Un is the system's environment at the time n. If the Un is not observable, we may consider to use the model: Xn+1 = F (Xn ; Un ); by somehow learning the function Un from the available data provided the unknown Un is generated from a deterministic system. Several non-stationary time series are tested using the above models. Satisfactory results have been obtained including free-run predictions and bifurcation diagram recovering. INTRODUCTION Recently there have been many discussions on predictions of non-stationary time series, e.g., [7,8,10]. To improve the predictions, we may need to know what are the mechanisms to produce the nonstationarity of time series. One of the main mechanisms which is quite obvious and we have understood is that the system's envi..