HOLT–WINTERS MODEL: MATHEMATICAL ASPECTS AND COMPUTER IMPLEMENTATION

Evaluation, modeling and forecasting of financial and economic indicators are the most complex problems while studying various economic phenomena. For the short-term forecasting of temporal series, the Brown model can be used. The Holt model can be applied if it is necessary to consider a trend without seasonality. However, the financial indicators studied often have the trend component and are subject to the seasonal fluctuations. Such processes can be adequately modeled by the temporal series including both the trend and the seasonal component (trend-seasonal temporal series). One of the most effective methods of modeling of trend-seasonal temporal series including the forecasting of economic phenomena indicators is the Holt–Winters model that is the evolution of Holt model. Its rather simple implementation in various packages of application software including the Excel electronic spreadsheets is one of the advantages of this model. However, when using this model, it is necessary to select the model’s parameters that can cause difficulties as the algorithm of this selection is not clear. In this paper, the authors analyzed possible algorithms used for the solution of similar tasks; however, their implementation is hardly suitable in the case under discussion. That is why the authors offer simple but rather effective algorithm including the minimization of the error functionality that is often used in the theory of artificial neural networks. The program implementation of this algorithm is rather simple and should not cause difficulties. The authors’ calculations showed that the particular set of model parameters can correspond to almost indistinguishable sets of expected model values and, therefore, the values of these parameters are nonspecific to the economic indicator under consideration.