Multiscale fluctuations and complexity synchronization of Bitcoin in China and US markets

Abstract Bitcoin appeared as a currency, but it is treated as a speculative product due to its violent fluctuation. The main purpose of this article is to find out the fluctuations similarities and differences between China and US Bitcoin markets, as well as Bitcoin market and stock market by Econophysics. We use the multiscale composite complexity synchronization (MCCS) correlation to study the complexity synchronization of Bitcoin price and stock indices fluctuations in those two markets. And we use the multifractal detrended fluctuation analysis (MFDFA) to analyze the inner fractal features of each time series’s small and large fluctuations. The corresponding shuffled time series are also utilized to do the above two kinds of analysis, in order to distinguish what lead to the complexity synchronization and multifractal properties, the different long-range correlations for the times series’ small and large fluctuations or the probability density functions for fluctuations of those nonstationary times series, or both of them. By this study, we find that small fluctuations have the strong memory and synchronization while big fluctuations possess the weak memory and synchronization, and the Bitcoin market has greater synchronicity than the stock market, and large fluctuations in China financial market are persistent while they are anti-persistent in US market.

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