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With the aggravation of the global economic crisis and inflation, the precious metals with safe-haven function have become more popular. An improved MF-DFA method is proposed to analyze price fluctuations of the precious metals market.…

Statistical Finance · Quantitative Finance 2020-06-30 Zhongjun Wang , Mengye Sun , A. M. Elsawah

Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…

Statistical Mechanics · Physics 2009-11-07 A. Z. Gorski , S. Drozdz , J. Speth

Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both…

Statistical Finance · Quantitative Finance 2016-10-25 Petr Jizba , Jan Korbel

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The…

Statistical Finance · Quantitative Finance 2025-06-24 Yaoyue Tang , Karina Arias-Calluari , M. N. Najafi , Michael S. Harré , Fernando Alonso-Marroquin

The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75\% of total market capitalisation and compare their evolution with that of a…

Statistical Finance · Quantitative Finance 2023-09-08 Esther Cabezas-Rivas , Felipe Sánchez-Coll , Isaac Tormo-Xaixo

This study investigates the volatility of daily Bitcoin returns and multifractal properties of the Bitcoin market by employing the rolling window method and examines relationships between the volatility asymmetry and market efficiency.…

Statistical Finance · Quantitative Finance 2021-02-18 Tetsuya Takaishi

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking…

Statistical Finance · Quantitative Finance 2022-08-23 Zhi-Qiang Jiang , Wen-Jie Xie , Wei-Xing Zhou , Didier Sornette

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

The spacing of nearest levels of the spectrum of a complex network can be regarded as a time series. Joint use of Multi-fractal Detrended Fluctuation Approach (MF-DFA) and Diffusion Entropy (DE) is employed to extract characteristics from…

Statistical Mechanics · Physics 2007-05-23 Huijie Yang , Fangcui Zhao , Longyu Qi , Beilai Hu

Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate…

Statistical Mechanics · Physics 2017-02-08 Longfeng Zhao , Wei Li , Chunbin Yang , Jihui Han , Zhu Su , Yijiang Zou , Xu Cai

This letter revisits the informational efficiency of the Bitcoin market. In particular we analyze the time-varying behavior of long memory of returns on Bitcoin and volatility 2011 until 2017, using the Hurst exponent. Our results are…

Statistical Finance · Quantitative Finance 2017-09-26 Aurelio F. Bariviera

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

Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the multifractal detrended fluctuation analysis, we obtain the…

Statistical Finance · Quantitative Finance 2020-04-16 Tetsuya Takaishi

We study recurrent patterns in volatility and volume for major cryptocurrencies, Bitcoin and Ether, using data from two centralized exchanges (Coinbase Pro and Binance) and a decentralized exchange (Uniswap V2). We find systematic patterns…

Trading and Market Microstructure · Quantitative Finance 2021-11-05 Peter Reinhard Hansen , Chan Kim , Wade Kimbrough

The relation between time series irreversibility and entropy production has been recently investigated in thermodynamic systems operating away from equilibrium. In this work we explore this concept in the context of financial time series.…

Statistical Finance · Quantitative Finance 2016-01-11 Lucas Lacasa , Ryan Flanagan

Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…

Data Analysis, Statistics and Probability · Physics 2008-04-07 Jan W. Kantelhardt

Stock markets can become inefficient due to calendar anomalies known as day-of-the-week effect. Calendar anomalies are well-known in financial literature, but the phenomena remain to be explored in econophysics. In this paper we use…

Statistical Finance · Quantitative Finance 2022-05-04 Darko Stosic , Dusan Stosic , Irena Vodenska , H. Eugene Stanley , Tatijana Stosic

On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…

Chaotic Dynamics · Physics 2025-02-26 Ritik Roshan Giri , Suchandan Kayal

Modelling financial time series as a time change of a simpler process has been proposed in various forms over the years. One of such recent approaches is called volatility homogenisation decomposition, and has been designed specifically to…

Statistical Finance · Quantitative Finance 2014-07-01 Paweł Fiedor , Odd Magnus Trondrud

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that…

Statistical Finance · Quantitative Finance 2011-05-24 Stanislaw Drozdz , Jaroslaw Kwapien , Pawel Oswiecimka , Rafal Rak