Biclustering high‐frequency financial time series based on information theory

Abstract

Clustering a large number of time series into relatively homogeneous groups is a well‐studied unsupervised learning technique that has been widely used for grouping financial instruments (say, stocks) based on their stochastic properties across the entire time period under consideration. However, clustering algorithms ignore the notion of biclustering, that is, grouping of stocks only within a subset of times rather than over the entire time period. Biclustering algorithms enable grouping of stocks and times simultaneously, and thus facilitate improved pattern extraction for informed trading strategies. While biclustering methods may be employed for grouping low‐frequency (daily) financial data, their use with high‐frequency financial time series of intra‐day trading data is especially useful. This paper develops a biclustering algorithm based on pairwise or groupwise mutual information between one‐minute averaged stock returns within a trading day, using jackknife estimation of mutual information (JMI). We construct a multiple day time series biclustering (MI‐MDTSB) algorithm that can capture refined and local comovement patterns between groups of stocks over a subset of continuous time points. Extensive numerical studies based on high‐frequency returns data reveal interesting intra‐day patterns among different asset groups and sectors.