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We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…

Statistical Mechanics · Physics 2008-12-10 J. -F. Muzy , D. Sornette , J. Delour , A. Arneodo

We study multifractal properties in time evolution of a single particle subject to repeated measurements. For quantum systems, we consider circuit models consisting of local unitary gates and local projective measurements. For classical…

Quantum Physics · Physics 2024-10-28 Kohei Yajima , Hisanori Oshima , Ken Mochizuki , Yohei Fuji

In this paper, we use the generalized Hurst exponent approach to study the multi- scaling behavior of different financial time series. We show that this approach is robust and powerful in detecting different types of multiscaling. We…

Statistical Finance · Quantitative Finance 2012-05-25 Jozef Barunik , Tomaso Aste , Tiziana Di Matteo , Ruipeng Liu

We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be…

Statistical Finance · Quantitative Finance 2014-04-10 Raffaello Morales , T. Di Matteo , Tomaso Aste

We present a multifractal analysis of time series data obtained by repeatedly running a single-qubit quantum circuit on IBM superconducting quantum computers, in which the measurement outcomes are recorded as the number of zeros. By…

Quantum Physics · Physics 2025-12-23 Mohammadreza Saghafi , Lamine Mili , Karlton Wirsing

Cryptocurrencies return cross-predictability and technological similarity yield information on risk propagation and market segmentation. To investigate these effects, we build a time-varying network for cryptocurrencies, based on the…

Statistical Finance · Quantitative Finance 2021-08-27 Li Guo , Wolfgang Karl Härdle , Yubo Tao

Cryptocurrencies return cross-predictability and technological similarity yield information on risk propagation and market segmentation. To investigate these effects, we build a time-varying network for cryptocurrencies, based on the…

Methodology · Statistics 2022-11-18 Li Guo , Wolfgang Karl Härdle , Yubo Tao

This work builds upon the long-standing conjecture that linear diffusion models are inadequate for complex market dynamics. Specifically, it provides experimental validation for the author's prior arguments that realistic market dynamics…

Statistical Finance · Quantitative Finance 2025-09-04 Igor Halperin

Extreme volatility, nonlinear dependencies, and systemic fragility are characteristics of cryptocurrency markets. The assumptions of normality and centralized control in traditional financial risk models frequently cause them to miss these…

Risk Management · Quantitative Finance 2025-07-15 Kiarash Firouzi

The presence of multifractality in a time series shows different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature…

Astrophysics of Galaxies · Physics 2018-05-21 A. Bewketu Belete , J. P. Bravo , B. L. Canto Martins , I. C. Leão , J. M. De Araujo , J. R. De Medeiros

We assess the applicability of rough volatility models to Bitcoin realized volatility using the normalised p-variation framework of Cont and Das (2024). Applying this model-free estimator to high-frequency Bitcoin data from 2017 to 2024…

Statistical Finance · Quantitative Finance 2025-09-30 Milan Pontiggia

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Stanislaw Drozdz , Jaroslaw Kwapien , Pawel Oswiecimka , Rafal Rak

We investigate multifractality in the Korean stock-market index KOSPI. The generalized $q$th order height-height correlation function shows multiscaling properties. There are two scaling regimes with a crossover time around $t_c =40$ min.…

Chaotic Dynamics · Physics 2009-11-10 Jae Woo Lee , Kyuoung Eun Lee , Per Arne Rikvold

In this paper we extend the known methodology for fitting stable distributions to the multivariate case and apply the suggested method to the modelling of daily cryptocurrency-return data. The investigated time period is cut into 10…

Applications · Statistics 2018-10-24 Szabolcs Majoros , András Zempléni

The price volatility of cryptocurrencies is often cited as a major hindrance to their wide-scale adoption. Consequently, during the last two years, multiple so called stablecoins have surfaced---cryptocurrencies focused on maintaining…

Asymmetric relationship between price and volatility is a prominent feature of the financial market time series. This paper explores the price-volatility nexus in cryptocurrency markets and investigates the presence of asymmetric volatility…

Statistical Finance · Quantitative Finance 2021-07-09 Shinji Kakinaka , Ken Umeno

In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…

Condensed Matter · Physics 2009-10-31 J. F. Muzy , J. Delour , E. Bacry

Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes (instead of…

Statistical Finance · Quantitative Finance 2008-12-02 Zhi-Qiang Jiang , Wei-Xing Zhou

In this study, we perform some analysis for the probability distributions in the space of frequency and time variables. However, in the domain of high frequencies, it behaves in such a way as the highly non-linear dynamics. The wavelet…

General Finance · Quantitative Finance 2024-11-22 Tatsuru Kikuchi

The paper analyzes the cryptocurrency ecosystem at both the aggregate and individual levels to understand the factors that impact future volatility. The study uses high-frequency panel data from 2020 to 2022 to examine the relationship…

Statistical Finance · Quantitative Finance 2024-04-09 Alessio Brini , Jimmie Lenz