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Inverse Forecasting Problems of Time Series in the Harmonic Basis

V. M. Balyk, E.V. Balyk, N.Q. Thuong, M.A. Osadchuk


In this article the problem of time series forecasting based on the inverse forecasting method is considered. The reverse forecast is implemented as a two-level algorithm. At the lower level, the trend of the investigated process is constructed in the class of harmonic polynomials. The polynomial parameters are chosen according to the condition of the mean-square error minimum. At the upper level, the forecasting values are selected for the entire depth of the forecast in accordance with the criterion of the mean-square forecasting error minimum. At the upper level, it is necessary to solve a multicriterion problem and in some cases this problem has a very high dimension. The method of global search for the minimum in the criterion space was developed for this class of problems and the convergence of the method was proved. High accuracy of forecasting was achieved as the result of using the method of inverse forecasting. This forecasting is more accurate and surpasses the quality of processes, obtained by using methods of processes self-organization.


statistical analysis, forecasting, time series, inverse forecasting, harmonic polynomials, trend component.

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