Calculation of numerical values of the functional extrapolator of a fractal L-Markov process with quasi-rational spectral density
Abstract
Calculation of numerical values of the functional extrapolator of a fractal L-Markov process with quasi-rational spectral density
Incoming article date: 25.12.2025Numerical values of the functional extrapolator of a fractal L–Markov process with a quasi-rational spectrum are obtained. The methods of correlation and regression analysis were used to calculate the predicted complex values for the lead time t. The analysis of the real and imaginary parts of the optimal extrapolator is carried out for all correct values of the lead time t. The coefficients of Pearson linear correlation and Kendall rank correlation are calculated, which indicate a high linear correlation between the real and imaginary parts of the extrapolator and their noticeable rank correlation. The representability of the optimal extrapolator for the lead time t in the form of a linear combination of the values of the fractal L–Markov process under study at five points of the L–boundary is proved. The calculated values of the beta coefficient and the Hurst index indicate the high reliability of the forecast constructed in the work.
Keywords: extrapolation, L – Markov process, fractality, trend tolerance, spectral characteristic, correlation and regression analysis, optimal extrapolator, risk