The work is devoted to the study of adaptive models of time series and the development of methods for their construction. The most problematic stage in the implementation of algorithms for time series forecasting methods is the identification of unknown parameters, on which the adequacy of the prediction depends. On the basis of economic data, a number of adaptive models have been studied: using exponential smoothing, Brown, Holt-Winters and Theil-Wage models, which take into account seasonality. It was found that the main difficulties arise in the selection of constant smoothing and the choice of coefficients, since no universal algorithm for their task exists. The paper proposes a method for integrating the adaptive method and the method of numerical optimization. As an optimization method, the non-gradient method was chosen - the Particle Swarm Optimization (PSO), the use of which provided less error in the final forecast and convergence in all applications. Algorithms for finding the parameters to be identified, and a predictive model based on real data are presented. It is shown that in some cases the proposed model has an advantage over other models of time series.