Neural network analysis in time series forecasting

Objectives . To build neural network models of time series (LSTM, GRU, RNN) and compare the results of forecasting with their mutual help and the results of standard models (ARIMA, ETS), in order to ascertain in which cases a certain group of models should be used. Methods . The paper provides a review of neural network models and considers the structure of RNN, LSTM, and GRU models. They are used for modeling time series in Russian macroeconomic statistics. The quality of model adjustment to the data and the quality of forecasts are compared experimentally. Neural network and standard models can be used both for the entire series and for its parts (trend and seasonality). When building a forecast for several time intervals in the future, two approaches are considered: building a forecast for the entire interval at once, and step-by-step forecasting. In this way there are several combinations of models that can be used for forecasting. These approaches are analyzed in the computational experiment. Results . Several experiments have been conducted in which standard (ARIMA, ETS, LOESS) and neural network models (LSTM, GRU, RNN) are built and compared in terms of proximity of the forecast to the series data in the test period. Conclusions . In the case of seasonal time series, models based on neural networks surpassed the standard ARIMA and ETS models in terms of forecast accuracy for the test period. The single-step forecast is computationally less efficient than the integral forecast for the entire target period. However, it is not possible to accurately indicate which approach is the best in terms of quality for a given series. Combined models (neural networks for trend, ARIMA for seasonality) almost always give good results. When forecasting a non-seasonal heteroskedastic series of share price, the standard approaches (LOESS method and ETS model) showed the best results.