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: X n+1 = F (X n ; U n); where U n is the system's environment at the time n. If the U n is not observable, we may consider to use the model: X n+1 = F (X n ; ^ U n); by somehow learning the function ^ U n from the available data provided the unknown U n 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.