Sample distribution function construction for non-stationary time-series forecasting

The method of statistical analysis and forecasting of non-stationary time-series is proposed on the basis of quasi-stationary criterion of sample distribution function and evolution equation with weighted average velocity. This method is applied to predict the time-series values outside of quasi-stationary limits. The concrete prognosis model is constructed for the case of cyclic time-series. The accuracy of forecast is analyzed for various discrete models of Liouville equation.