基于MF-ADCCA方法的比特币量价关系多重分形特征研究

Research on multifractal characteristics of Bitcoin price-volume relationship based on MF-ADCCA method

本文使用MF-ADCCA方法实证分析了比特币量价关系的非对称多重分形特征,结果表明:比特币流动性越大,波动越大,收益率和交易量交叉相关性的多重分形程度越强,且这种多重分形特征来源于反持续性和厚尾分布,厚尾分布对多重分形特征的贡献更大。量价关系在不同涨跌趋势时的非对称性程度具有阶段性特征,当比特币价格较低且相对平稳时,无论是收益率上涨还是交易量变化率上涨,量价交叉相关性在小幅波动时持续性更强,大幅波动的反持续性更强;而在价格暴涨暴跌剧烈波动并且交易量变化率下跌时,量价交叉相关性持续性更强。通过滑动窗技术研究比特币量价关系局部多重分形特征,发现量价交叉相关性的局部时变Hurst指数小于0.5;随着时间的推移,量价交叉相关性的局部时变多重分形程度加强。

At present,as an emerging virtual financial asset,cryptocurrencies have attracted increasing attention from scholars,public investors,and financial risk managers.Since the birth of Bitcoin(BTC),the first cryptocurrency in 2009,the cryptocurrency market has developed rapidly with continuous innovation and expansion in scale.As of November 21,2020,the type of global cryptocurrencies reached 7,731 in the world,with 385 exchanges and 33289 trading markets and a total market cap of 3.473 trillion yuan.Among these cryptocurrencies,the market cap of BTC ranks first,accounting for 65.2%of the total market cap of cryptocurrencies,and the daily turnover exceeds 10 billion US dollars.Therefore,taking BTC as the representative of cryptocurrency assets,this paper explores the multifractal characteristics of cross-correlation between BTC′s volume and price.Research on the relationship between the volume and price of financial assets is not only helpful to deepen the understanding of financial market structure and understand how information flows into the market but can also reflect the relationship between supply and demand in the financial market to judge and predict the trend of the whole financial market.As an emerging financial asset,cryptocurrencies show characteristics that are different from those of traditional assets.For example,cryptocurrencies generally have higher returns but they fluctuate sharply.Studying the price fluctuation of cryptocurrencies and the relationship between volume and price can avoid investment risk and obtain more information about the financial market.This paper selects the daily closing price and trading volume of BTC from December 27,2013 to December 31,2019 as the research object,with a total of 2196 pairs of data.First,the logarithmic returns and the change rate of trading volume of BTC are calculated.Second,according to the price and trading volume,the whole sample is divided into two sub-samples to further study the impact of liquidity and volatility on the cross-correlation between volume and BTC price.In the empirical analysis,MFDCCA method is used to study the multifractal characteristics of BTC price-volume relationship,and the original data were randomly shuffled and phase randomized to study the source of the multifractal characteristics of the price-volume relationship.Then,the MF-ADDCA method is used to analyze the asymmetric multifractal characteristics of BTC price-volume relationship and calculate the asymmetric degree of price-volume cross-correlation under different trends.Finally,combined with the sliding window method,the local dynamic timevarying characteristics of BTC price-volume cross-correlation are investigated.The results show that:(1)the price-volume cross-relationship of BTC has asymmetric multifractal characteristics and has antipersistence characteristics.The multifractal degree of price-volume cross-relationship varies in different stages,that is,when the liquidity of BTC is stronger,the price fluctuation is more intense,and the multifractal degree of price-volume relationship is stronger.However,the lower the liquidity,the weaker the multifractal degree.(2)The multifractal characteristics of BTC price-volume crosscorrelation are affected by the anti-persistence and fat-tailed distribution,and the fat-tailed distribution has a greater impact on the multifractal strength.(3)BTC price-volume cross-correlation has phased differences in various trends.When the BTC price is relatively low and stable,whether returns rises or the rate of change in trading volume rises,the price-volume cross-correlation is more persistent in small fluctuations,and the anti-persistence of large fluctuations is stronger.Meanwhile,the price rises and falls sharply and the change rate of trading volume falls;thus,price-volume cross-correlation is more persistent.Finally,by using the sliding window method to study the local multifractal characteristics of BTC price-volume relationship,the local time-varying Hurst index of price-volume cross-correlation is found to be less than 0.5,and the local time-varying Hurst index shows phased changes.Over time,the local time-varying multifractal degree of the cross-correlation of BTC volume and price has strengthened.Generally,the price-volume relationship of BTC shows asymmetric nonlinear dependence.The study in price-volume relationship cannot be limited to the traditional linear paradigm but is based on fractal nonlinear theory to grasp the price-volume dependence structure of BTC more accurately.The change in BTC price-volume relationship can be used as reference in the research of cryptocurrency portfolio.However,the relationship between multi-asset and potential risk changes must still be explored further.