基于MFXDMA方法的加密货币和中国股市间的多重分形交叉相关性研究

加密货币这一新兴的金融市场目前引起了学者的广泛关注。本文主要基于多重分形降趋移动平均交叉相关分析法(MFXDMA)，以4类加密货币(比特币、以太坊、瑞波币和莱特币)、上证指数和恒生指数为研究对象，实证分析了加密货币单一市场、交叉市场间收益率的多重分形特征，以及加密货币和上证指数、恒生指数交叉相关性的多重分形特征。实证结果表明，比特币、以太坊、瑞波币和莱特币各单独市场的收益率具有长记忆性、非对称的多重分形特征。4个加密货币市场中以太坊的市场效率最强，而比特币的市场效率最弱。加密货币市场对内地股市和香港股市产生了一定影响，市场间的交叉相关持续性增强。通过对比特币、比特币和以太坊交叉市场采用中心和前向移动平均法进行对比分析，实验表明本文使用后向移动平均法的结果是稳健的。最后通过滑动窗技术，研究了单一市场和跨市场相关性、波动函数的时变特征，结果表明比特币和以太坊，上证指数和恒生指数时变特征具有一定的相似性，并且上证指数比恒生指数更易受加密货币市场的影响。

Multifractal Cross-Correlation between Cryptocurrency and Chinese Stock Market Based on MFXDMA Method

Cryptocurrency, an emerging financial market, has attracted extensive attention of scholars. The traditional research on cryptocurrency is often limited to the cryptocurrency market, and the research on the correlation between cryptocurrency and China’s stock market is relatively lacking.Based on the multifractal moving average cross-correlation analysis (MFXDMA), four types of cryptocurrencies (Bitcoin, Ethereum, Ripple and Litecoin), Shanghai Stock Exchange Index and Hang Seng Index are taken as the research objects, empirically analyzes the multifractal characteristics of the returns between the cryptocurrency single market and cross-market, and at the same time the multifractal characteristics of the cross-correlation of cryptocurrencies and the Shanghai Stock Index and the Hang Seng Index is focused on. The empirical results show that the returns of the individual markets of Bitcoin, Ethereum, Ripple, and Litecoin have long-term memory, asymmetric multifractal characteristics. Among the four cryptocurrencies markets, Ethereum is the most efficient, while Bitcoin is the least efficient. The cryptocurrency market has had a certain impact on the mainland stock market and Hong Kong stock market, and the cross-correlation between the markets has been strengthened, it also shows the asymmetrical multifractal characteristics.In the empirical analysis of the correlation between Bitcoin and China’s stock market, The MFXDMA method is compared with the commonly used MFXDFA and MFSMXA multifractal methods, and it is found that MFXDMA and MFSMXA have achieved similar results.By comparing and analyzing the cross-market of Bitcoin, Bitcoin, and Ethereum using the central and forward moving average method, experiments show that the results of this paper using the backward moving average are robust. Finally, the time-varying characteristics of single market and cross-market correlation and volatility function are studied by using sliding window technology. The results show that Bitcoin and Ethereum, Shanghai Stock Exchange Index and Hang Seng index have certain similarity in time-varying characteristics, and Shanghai Stock Exchange Index is more susceptible to the impact of cryptocurrency market than Hang Seng Index. The correlation between cryptocurrency and China’s stock market is studied, which is of great significance for the risk aversion of China’s stock market. It can be used as a reference for the cross-market portfolio research of cryptocurrency and China’s stock market and the financial risk supervision of relevant departments.