Current Approaches to Forecasting Non-Stationary Time Series

The article studies current methods of foresting non-stationary time series effective to analyze social and economic systems, finance markets and other fields with high rate of uncertainty. Comparative analysis of classical approaches (ARIMA, GARCH) and their modifications was carried out as they take into account structural changes, non-linear dependences and exogenous factors. Special attention was paid to neural network methods, including LSTM, transformers (Informer, Autoformer) and their hybrid versions that demonstrate high efficiency working with long successions. Apart from that adaptive methods were studied such as sliding window and their integration with machine learning to raise accuracy of forecasting in conditions of uncertainty. The research includes critical analysis of restrictions of classical models ARIMA and GARCH, the review of current architecture of neural nets for time series, practical aspects of choosing models depending on data characteristics, promising lines in developing methods, including adaptive algorithms and ensemble approaches.