标题： 多重分形性及其在数字货币市场中的来源 显示英文标题

标题： Multifractality and its sources in the digital currency market

摘要： 多分形性在时间序列分析中表征了多个标度指数的存在，表明存在异质的时间结构和超越简单单分形模型的复杂动态行为。 在数字货币市场背景下，多分形特性是由于回报的长程时间相关性和重尾分布之间的相互作用而产生的，反映了复杂的市场微观结构和交易者互动。 将多分形分析纳入加密货币价格动态的建模中，可以增强对市场无效性的理解，可能改善波动率预测，并有助于检测关键转变或制度转移。 基于多分形交叉相关分析（MFCCA），其特殊情形是多分形去趋势波动分析（MFDFA），作为量化多分形性的最常用实用工具，在本研究中应用了一种最近提出的用于分离时间序列中多分形性来源的方法，以对数字市场中最具代表性的工具进行分析。 它们包括比特币（BTC）、以太坊（ETH）、去中心化交易所（DEX）和非同质化代币（NFT）。 结果表明重尾在生成广泛的多分形谱中起着重要作用。 然而，它们也明确表明，多分形性的主要来源是序列中的时间相关性，没有这些相关性，多分形性就会消失。 值得注意的是，这些时间相关性在很大程度上并不依赖于波动分布尾部的厚度。 在此数字货币市场背景下做出的这些观察，为所提出的分离时间序列中多分形性来源的方法论的有效性提供了进一步的有力论证。 显示英文摘要

摘要： 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 currency markets, multifractal properties arise due to the interplay of long-range temporal correlations and heavy-tailed distributions of returns, reflecting intricate market microstructure and trader interactions. Incorporating multifractal analysis into the modeling of cryptocurrency price dynamics enhances the understanding of market inefficiencies, may improve volatility forecasting and facilitate the detection of critical transitions or regime shifts. Based on the multifractal cross-correlation analysis (MFCCA) whose spacial case is the multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical tools for quantifying multifractality, in the present contribution a recently proposed method of disentangling sources of multifractality in time series was applied to the most representative instruments from the digital market. They include Bitcoin (BTC), Ethereum (ETH), decentralized exchanges (DEX) and non-fungible tokens (NFT). The results indicate the significant role of heavy tails in generating a broad multifractal spectrum. However, they also clearly demonstrate that the primary source of multifractality are temporal correlations in the series, and without them, multifractality fades out. It appears characteristic that these temporal correlations, to a large extent, do not depend on the thickness of the tails of the fluctuation distribution. These observations, made here in the context of the digital currency market, provide a further strong argument for the validity of the proposed methodology of disentangling sources of multifractality in time series.