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arXiv · 2309.04206

Variable order porous media equations: Application on modeling the S&P500 and Bitcoin price return

Yaoyue Tang·Fatemeh Gharari·Karina Arias-Calluari·Fernando Alonso-Marroquin·M. N. Najafi
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Abstract

This article reveals a specific category of solutions for the $1+1$ Variable Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO $q$-Gaussian functions, granting them significant versatility in their application to various real-world systems, such as financial economy areas spanning from conventional stock markets to cryptocurrencies. The VO $q$-Gaussian functions provide a more robust expression for the distribution function of price returns in real-world systems. Additionally, we analyzed the temporal evolution of the anomalous characteristic exponents derived from our study, which are associated with the long-range memory in time series data and autocorrelation patterns.

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Yaoyue Tang, Fatemeh Gharari, Karina Arias-Calluari, Fernando Alonso-Marroquin, M. N. Najafi. 2023-09-08. Variable order porous media equations: Application on modeling the S&P500 and Bitcoin price return. https://arxiv.org/abs/2309.04206

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