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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 in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital…

Statistical Finance · Quantitative Finance 2025-10-16 Stanisław Drożdż , Robert Kluszczyński , Jarosław Kwapień , Marcin Wątorek

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

This paper studies of the multifractal dynamics in 84 cryptocurrencies. It fills an important gap in the literature, by studying this market using two alternative multi-scaling methodologies. We find compelling evidence that…

Statistical Finance · Quantitative Finance 2020-06-16 Aurelio F. Bariviera

In this paper, we explore some stylized facts of the Bitcoin market using the BTC-USD exchange rate time series of historical intraday data from 2013 to 2020. Bitcoin presents some very peculiar idiosyncrasies, like the absence of…

Statistical Finance · Quantitative Finance 2024-09-04 F. N. M. de Sousa Filho , J. N. Silva , M. A. Bertella , E. Brigatti

The finite sample effect on the Hurst exponent (HE) of realized volatility time series is examined using Bitcoin data. This study finds that the HE decreases as the sampling period $\Delta$ increases and a simple finite sample ansatz…

Statistical Finance · Quantitative Finance 2025-11-06 Tetsuya Takaishi

Based on 1-minute price changes recorded since year 2012, the fluctuation properties of the rapidly-emerging Bitcoin (BTC) market are assessed over chosen sub-periods, in terms of return distributions, volatility autocorrelation, Hurst…

Statistical Finance · Quantitative Finance 2018-07-20 Stanisław Drożdż , Robert Gębarowski , Ludovico Minati , Paweł Oświęcimka , Marcin Wątorek

We perform a systematic investigation on the components of the empirical multifractality of financial returns using the daily data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. The temporal structure and…

Statistical Finance · Quantitative Finance 2009-12-24 Wei-Xing Zhou

In the work, a comparative correlation and fractal analysis of time series of Bitcoin crypto currency rate and community activities in social networks associated with Bitcoin was conducted. A significant correlation between the Bitcoin rate…

Statistical Finance · Quantitative Finance 2019-05-06 Lyudmyla Kirichenko , Vitalii Bulakh , Tamara Radivilova

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

In this paper, we analyze the time-series of minute price returns on the Bitcoin market through the statistical models of generalized autoregressive conditional heteroskedasticity (GARCH) family. Several mathematical models have been…

Statistical Finance · Quantitative Finance 2021-02-01 Irena Barjašić , Nino Antulov-Fantulin

We study the temporal evolution of the holding-time distribution of bitcoins and find that the average distribution of holding-time is a heavy-tailed power law extending from one day to over at least $200$ weeks with an exponent…

Trading and Market Microstructure · Quantitative Finance 2024-01-10 Didier Sornette , Yu Zhang

Using the asymmetric stochastic volatility model, this study investigates the day-of-the-week and holiday effects on the returns and volatility of Bitcoin from January 1, 2013 to August 31, 2019; in this context, we also discuss the…

Statistical Finance · Quantitative Finance 2022-10-17 Noriyuki Kunimoto , Kazuhiko Kakamu

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

This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin time…

Statistical Finance · Quantitative Finance 2020-09-16 Tetsuya Takaishi , Takanori Adachi

A reputation of high volatility accompanies the emergence of Bitcoin as a financial asset. This paper intends to nuance this reputation and clarify our understanding of Bitcoin's volatility. Using daily, weekly, and monthly closing prices…

Statistical Finance · Quantitative Finance 2021-03-02 Nassim Dehouche

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

The S&P 500 index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past years, Bitcoin has also grown in popularity and adoption. The paper aims to analyze the daily return…

Statistical Finance · Quantitative Finance 2024-06-11 A. H. Nzokem

Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…

Statistical Finance · Quantitative Finance 2013-11-19 Raoul Golan , Austin Gerig

We show Bitcoin implied volatility on a 5 minute time horizon is modestly predictable from price, volatility momentum and alternative data including sentiment and engagement. Lagged Bitcoin index price and volatility movements contribute to…

Statistical Finance · Quantitative Finance 2020-10-30 Faizaan Pervaiz , Christopher Goh , Ashley Pennington , Samuel Holt , James West , Shaun Ng
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