How does a systematic time-dependence of the diffusion coefficient D (t) affect the ergodic
and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this …

Abstract The Black–Scholes equation is one of the most important partial differential
equations governing the value of financial derivatives in financial markets. The Black …

Market inefficiency is a latent concept, and it is difficult to be measured by means of a single
indicator. In this paper, following both the adaptive market hypothesis (AMH) and the fractal …

Little attention has been devoted to the long memory among the different data features
considered for clustering time series. Following previous literature, we measure the long …

Assuming that stock prices follow a multi-fractional Brownian motion, we estimated a time-
varying Hurst exponent (ht). The Hurst value can be considered a relative volatility measure …

In this paper, by considering a model-based approach for conditional moment estimation, a
nonparametric test was performed to study the long-memory property of higher moments …

This research focuses on utilizing the Hurst exponent (ℎ) as a critical measure of relative
volatility, with a specific emphasis on its ideal value of 0.5. The paper introduces an …

Fractional Brownian motion has become a standard tool to address long-range dependence
in financial time series. However, a constant memory parameter is too restrictive to address …

This study aims to estimate the information efficiency of financial markets based on the Hurst
exponent, with a focus on the S&P 500 index. The approach involves using statistical …