Nonstationary time series have features that make them interesting objects of physics and technology. The nonstationarity is due to the presence of chaotic dynamics in the behavior of the time series. Chaotic dynamics is determined by the specifics of the processes in the dynamic system under study, associated with the presence of unstable components. To predict non-stationary time series, it is proposed to use the moving window method, which allows determining the structural components of the time series, attractors or characteristic figures. The attractor from the found set, which is close to the figure of the time series in the last window, is used to predict a non-stationary time series. It is established that the reliability of forecasting is directly proportional to the number of similar attractors. Software has been developed in Python to determine the attractors of a non-stationary time series. The work of the software is implemented in forecasting the financial time series of Sberbank, Brent oil price for example. The results of a computational experiment show the effectiveness of using the moving window method for forecasting non-stationary time series in semi-structured systems. #COMESYSO1120.