{"title":"Multifractality and sample size influence on Bitcoin volatility patterns","authors":"Tetsuya Takaishi","doi":"10.1016/j.frl.2024.106683","DOIUrl":null,"url":null,"abstract":"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 <mml:math altimg=\"si73.svg\" display=\"inline\"><mml:mi>Δ</mml:mi></mml:math> increases and a simple finite sample ansatz closely fits the HE data. We obtain HE values of <mml:math altimg=\"si2.svg\" display=\"inline\"><mml:mrow><mml:mi>Δ</mml:mi><mml:mo>→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>, which is smaller than 1/2, indicating rough volatility. The relative error is found to be 1% for the widely used five-minute realized volatility. Performing a multifractal analysis, we find that multifractality in the realized volatility time series is smaller than that of the price-return time series.","PeriodicalId":12167,"journal":{"name":"Finance Research Letters","volume":"14 1","pages":""},"PeriodicalIF":7.4000,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finance Research Letters","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1016/j.frl.2024.106683","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
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 Δ increases and a simple finite sample ansatz closely fits the HE data. We obtain HE values of Δ→0, which is smaller than 1/2, indicating rough volatility. The relative error is found to be 1% for the widely used five-minute realized volatility. Performing a multifractal analysis, we find that multifractality in the realized volatility time series is smaller than that of the price-return time series.
期刊介绍:
Finance Research Letters welcomes submissions across all areas of finance, aiming for rapid publication of significant new findings. The journal particularly encourages papers that provide insight into the replicability of established results, examine the cross-national applicability of previous findings, challenge existing methodologies, or demonstrate methodological contingencies.
Papers are invited in the following areas:
Actuarial studies
Alternative investments
Asset Pricing
Bankruptcy and liquidation
Banks and other Depository Institutions
Behavioral and experimental finance
Bibliometric and Scientometric studies of finance
Capital budgeting and corporate investment
Capital markets and accounting
Capital structure and payout policy
Commodities
Contagion, crises and interdependence
Corporate governance
Credit and fixed income markets and instruments
Derivatives
Emerging markets
Energy Finance and Energy Markets
Financial Econometrics
Financial History
Financial intermediation and money markets
Financial markets and marketplaces
Financial Mathematics and Econophysics
Financial Regulation and Law
Forecasting
Frontier market studies
International Finance
Market efficiency, event studies
Mergers, acquisitions and the market for corporate control
Micro Finance Institutions
Microstructure
Non-bank Financial Institutions
Personal Finance
Portfolio choice and investing
Real estate finance and investing
Risk
SME, Family and Entrepreneurial Finance