We use the statistical properties of Shannon entropy estimator and Kullback–Leibler divergence to study the predictability of ultra-high frequency financial data. We develop a statistical test for the predictability of a sequence based on empirical frequencies. We show that the degree of randomness grows with the increase of aggregation level in transaction time. We also find that predictable days are usually characterized by high trading activity, i.e., days with unusually high trading volumes and the number of price changes. We find a group of stocks for which predictability is caused by a frequent change of price direction. We study stylized facts that cause price predictability such as persistence of order signs, autocorrelation of returns, and volatility clustering. We perform multiple testing for sub-intervals of days to identify whether there is predictability at a specific time period during the day.

中文翻译：

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超高频下的价格可预测性：基于熵的随机性检验


我们使用 Shannon 熵估计器和 Kullback-Leibler 散度的统计特性来研究超高频金融数据的可预测性。我们开发了一个基于经验频率的序列可预测性的统计检验。我们表明，随机性程度随着交易时间聚合级别的增加而增加。我们还发现，可预测的日子通常以高交易量为特征，即交易量和价格变化次数异常高的日子。我们发现一组股票的可预测性是由价格方向的频繁变化引起的。我们研究导致价格可预测性的程式化事实，例如订单信号的持续性、回报的自相关和波动率聚类。我们对子间隔的天数执行多次测试，以确定在一天中的特定时间段是否存在可预测性。