Clustering high-frequency financial time series based on information theory

Clustering large financial time series data enables pattern extraction that facilitates risk management. The knowledge gathered from unsupervised learning is useful for improving portfolio optimization and making stock trading recommendations. Most methods available in the literature for clustering financial time series are based on exploiting linear relationships between time series. However, prices of different assets (stocks) may have non-linear relationships which may be quantified using information based measures such as mutual information (MI). To estimate the empirical mutual information between time series of stock returns, we employ a novel kernel density estimator (KDE) based jackknife mutual information estimation (JMI), and compare it with the widely-used binning method. We then propose an average distance gradient change algorithm and an algorithm based on the average silhouette criterion that use pairwise and groupwise MI of high-frequency financial stock returns. Through numerical studies, we provide insights into the impact of the clustering on asset allocation and risk management based on the nonlinear information structure of the US stock market.