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Analysis of the approximation of time series trend and forecasting based on it

The empirical analysis of building the time series model as a combination of a linear function of time, the partial sum of the Fourier series and specific procedures of the Fourier coefficients has been considered in the report. The experiments have been conducted with real data of different nature. It is noted that the consistent series expansion into the Fourier sine and cosine transformations and further optimization of the coefficients give a better result than without optimization. On the basis of this expansion a number of experiments to estimate the forecast horizon have been carried out.