A statistical test of market efficiency based on information theory
利用香农熵从价格收益率时间序列中提取信息量，推导出市场有效性假设下的统计分布，构建检验方法，并应用于股票指数、个股和加密货币数据。
We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time series. By deriving the exact and the asymptotic distribution of this market information indicator in the case where the efficient market hypothesis holds, we develop a statistical test of market efficiency. We apply it to a real dataset of stock indices, single stocks, and cryptocurrencies, for which we are able to determine at each date whether the efficient market hypothesis is to be rejected, with respect to a given confidence level.