Methods of analyzing the nonstationary time series with implicit changes in their properties

The problems of analysis of the nonstationary time series with explicit and implicit changes in their properties were discussed. The main approaches and methods of analysis of the nonstationary processes were described. Consideration was given to the trend-stationary and difference-stationary processes. The algorithms to determine the process type hinge on verifying hypotheses like "initial process is a DS-process (TS-process)" against the alternative ones. The notions of false regression and cointegration were discussed. The problems arising at analysis of the varying-property processes and methods of their solution were reviewed. Consideration was given to the cases of explicit and implicit changes and algorithms of detection in the current and a posteriori modes.