Method of Integration of Formal Forecasting Methods into Data Assimilation on the Example of Autoregressive Time Series

The article describes the method developed for integration of formal methods of time series (TS) forecasting (such as autoregressive integrated moving average (ARIMA), singular spectrum analysis (SSA), group method of data handling (GMDH), artificial recurrent neural network with long short-term memory (LSTM)) into the Data Assimilation (DA) technique. The method can be used in cases where mathematical model of the dynamic system generating the TS is not known (for example, TS consisting of economic indicators). The performance of the integration method is confirmed by a forecasting of a TS generated using AR(p) process of order p, where $p = \overline {1,10} $. The comparative analysis of the forecasting accuracy of the method against ARIMA method was carried out. The developed technique showed high accuracy, except for a small set of parameters that lead to an increase in the forecasting error. This, from our point of view, is due to the local features of the predicted TS. The analysis shows that the developed method shows higher forecasting accuracy in comparison with formal methods.