This paper describes an approach that is able to fix difference in multifractal behaviour of various World Stock Indexes. The approach is beneficial for the forecasting and simulations of the most European and Asian stock indexes. Multifractal analysis is provided using the so-called Wavelet Transform Modulus Maxima approach, which involves two basic aspects:
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.
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