Stock Market Structural Changes Discovering Helical Structure of Volatility Wave Fourier Image/ Akciju tirgu struktūras izmai?u atklā?ana, izpētot volatilitātes vi??u Furjē attēla spirālveida struktūru/ Выявление структурных изменений фондовых рынков, исследующих спиралевидную структуру Фурье образа волн волатильности

摘要

This paper explores an alternative volatility estimation approach discovering the helical structure of Fourier coefficients of volatility wave. Volatility wave is calculated by using wavelet decomposition with consequent logarithmic variance indicator estimation for each decomposed part of the signal and subsequent volatility matrix transform in a specified way. Further, using discrete Fourier transform the Fourier image of obtained volatility wave is analyzed. The Fourier image coefficients of the transformed volatility indicator have a clear helical (spiral) structure that evolves in time. This brings a new understanding of volatility and its evolution process from signal theory (and wavelet theory) perspective. We have found some regularity in the volatility evolution process. The minimum total distance indicator between Fourier coefficients is proposed as a measure of such regularity. This indicator has a nature of volatility lower bound.