Abstract

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 describe 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 was obtained. A new criterion for the algorithm stopping was 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. 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, were revealed.