Volatility Modeling of Time Series Using Fractal and Self-Similarity Models

William Kubin, University of Texas at El Paso


The study uses various methods to compare the scaling parameters and long-term memory behavior of financial and geophysical time series. The Cantor Detrended Fluctuation Analysis (CDFA) method is proposed to provide more accurate estimates of Hurst exponents. The CDFA method is applied to real-time series and the results are verified. The study also analyzes the memory behavior of daily Covid-19 cases before and after the announcement of effective vaccines. Low and high-frequency data’s influence on the Hurst Index estimation is investigated, and a new PCDFA method is proposed. The stability of the Dow Jones Industrial Average is analyzed using a multi-scale normalized diffusion entropy and conditional diffusion entropy. The study aims to investigate memory behavior in time series using deep learning techniques in future work.

Subject Area

Applied Mathematics|Mathematics

Recommended Citation

Kubin, William, "Volatility Modeling of Time Series Using Fractal and Self-Similarity Models" (2023). ETD Collection for University of Texas, El Paso. AAI30487276.