The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets.

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基于熵的股票市场深度度量方法

这项研究的目的是调查市场深度作为股票市场流动性的维度。引入并利用了一种完全基于Shannon信息熵的高频数据市场深度测量方法。所提出的基于熵的市场深度指标得到了推断交易发起者的算法的支持。这一新指标似乎是一种很有前途的流动性指标。新指标可以直接衡量市场熵和市场流动性。时间戳为距华沙证券交易所（WSE）最接近的秒的实数据的经验实验的结果证实，新代理使我们能够有效地比较不同股票的市场深度和流动性。进行稳健性测试和统计分析。此外，提供日内季节性评估。结果表明，基于熵的方法可以被视为吉利的市场深度和流动性的代理，并为金融市场中的理论和经验分析提供了直观的基础。