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E.A.Pitukhin, L.V.Shchegoleva

The paper is devoted to the construction of the algorithm of piecewise linear approximation of time series, the distinctive feature of which is the preservation of sharp "peaks" and data outliers. As a basis, the iterative algorithm of piecewise linear approximation proposed by E. K. Bely in 1994 was taken. This algorithm was used to smooth the experimental medical data on respiratory function of the lungs. The algorithm was modified to significantly increase the precision and to reduce the number of iterations. The rule of determining the optimal number of time series splitting by the minimum of the adjusted coefficient of determination is obtained. A new criterion for the algorithm stopping is proposed. As a testing data, the two-factor function of Weierstrass-Mandelbrot was used, which allows to generate data in a wide range of shapes and variability. The time series obtained by the Weierstrass-Mandelbrot function are nonstationary and have fractality. As the output parameters of the algorithm, various known approximation quality metrics were considered, for example, the mean absolute percentage error, mean squared error, adjusted coefficient of determination, and so on. In numerical experiment, the control parameters of the function were set by random variables with a uniform distribution law. The estimations of probability densities of the output parameters of the algorithm were obtained by the Monte Carlo method. The convergence of the approximation algorithm was studied and the regions of shape and variability parameters, at which the algorithm converges, are revealed. An empirical formula in the form of a linear function for the dependence of the optimal number of intervals from the series length is obtained. The quality of the algorithm of approximation was also studied on real data of quotations of currency pairs.