Stationarity and nonstationarity in time series analysis

In this paper we introduce a new class of methods to test, model and describe nonstationary processes. To frame these methods, we generalize the dynamical description of autonomous systems to the case of nonautonomous systems. Of particular interest are systems for which the driving force is recurrent. For these systems we describe a method to find recurrences and to improve the statistics in reconstructing the time series and, consequently, to improve the predictability. Another objective is a proper description of the nonstationarity. All these methods are applied to four examples.