The monograph describes a technique for integrating formal methods of time series forecasting and Data Assimilation. This technique provides a correction of previously predicted values at subsequent time points based on a comparison of the predicted and observed values of the time series at a given time point. The monograph presents mathematical, algorithmic and software implementation for forecasting and correcting the forecast of time series. The monograph describes formal methods for time series forecasting, such as the autoregressive moving average method, the singular spectrum analysis method, the group method of data handling, and the method based on neural networks. The authors describe a method for correcting the forecast of time series «Data Assimilation «using the Kalman filter and the Ensemble Kalman filter. The monograph describes the study of the need to develop a methodology for integrating formal methods of time series forecasting and the Data Assimilation. The performance of the presented method, developed by the authors, is demonstrated on example of the Lorenz system in comparison with the classical data assimilation. The monograph provides an example of the use of the developed algorithmic, mathematical and software for time series forecasting on the example of three data sets ”Air Passengers solar activity and sets dollar and euro exchange rates against the ruble.