The article describes the method developed by the authors for integration of formal methods of time series (TS) forecasting (autoregressive integrated moving average (ARIMA), singular spectrum analysis, group method of data handling, artificial recurrent neural network with long short-term memory) into the Data Assimilation (DA), 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 proposed integration method is illustrated on the example of forecasting TS named "Air Passengers" using the DA method based on the ensemble Kalman filter with integrated ARIMA method. Estimations of the accuracy of "Air Passengers" TS forecasts is calculated using ARIMA and the proposed integration method. Article discusses the advantages and disadvantages of the proposed method for integrating formal TS forecasting methods into the DA and also directions for its further improvement.