英文标题：
《Chaos and Order in the Bitcoin Market》
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作者：
Josselin Garnier, Knut Solna
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最新提交年份：
2019
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英文摘要：
The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that the bitcoin price exhibits a very interesting multi-scale correlation structure. This structure can be described by a power-law behavior of the variances of the returns as functions of time increments and it can be characterized by two parameters, the volatility and the Hurst exponent. These power-law parameters, however, vary in time. A new notion of generalized Hurst exponent is introduced which allows us to check if the multi-fractal character of the underlying signal is well captured. It is moreover shown how the monitoring of the power-law parameters can be used to identify regime shifts for the bitcoin price. A novel technique for identifying the regimes switches based on a goodness of fit of the local power-law parameters is presented. It automatically detects dates associated with some known events in the bitcoin market place. A very surprising result is moreover that, despite the wild ride of the bitcoin price in recent years and its multi-fractal and non-stationary character, this price has both local power-law behaviors and a very orderly correlation structure when it is observed on its entire period of existence.
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中文摘要：
近年来，比特币价格飙升，也呈现出快速衰退的阶段。在本文中，我们讨论了这种新型加密货币市场在多大程度上可以被视为经典或半有效市场的问题。利用新颖而稳健的多重分形特性估计工具表明，比特币价格呈现出非常有趣的多尺度相关结构。这种结构可以用收益率方差作为时间增量函数的幂律行为来描述，并且可以用两个参数来表征，即波动率和赫斯特指数。然而，这些幂律参数随时间而变化。引入了广义Hurst指数的新概念，它允许我们检查底层信号的多重分形特征是否被很好地捕获。此外，本文还展示了如何使用幂律参数监测来识别比特币价格的制度变迁。提出了一种基于局部幂律参数拟合优度的状态开关识别新方法。它自动检测与比特币市场中某些已知事件相关的日期。此外，一个非常令人惊讶的结果是，尽管近年来比特币价格狂飙起伏，且其具有多重分形和非平稳特征，但从其整个存在期来看，该价格既具有局部幂律行为，又具有非常有序的相关结构。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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