Clustering high‐frequency financial time series based on information theory

Abstract

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.

The Cryptocurrency Market in Transition before and after COVID-19: An Opportunity for Investors?

“…In [ 1 ], a Pearson correlation matrix of 200 and 400 stocks from the CSI 300 and index, respectively, was used to find an optimized portfolio following the Markowitz optimization scheme. Instead of using Pearson method, Liu et al’s paper used an interesting alternative method Mutual Information to generate a distance metric to take account of non-linear effects in intra-day S&P stock data [ 25 ]. Other methods to estimate the correlation coefficients (i.e., Wavelet coherence, Fast Fourier Transform) and construct correlation-based networks (i.e., PMFG, threshold method) were introduced in several studies [ 2 , 11 , 26 ].…”

“…There is also a concern with respect to the use of Pearson correlation for clustering problems. In particular, although this correlation metric has been applied widely in the existing literature and proposed various findings in the financial markets [ 2 , 21 , 22 ], it is sensitive to outliers [ 58 ] and cannot capture non-linear relationships that might cause misleading results [ 25 ]. Consequently, this adversely affects the clustering results.…”

“…Another future plan which is worth taking into consideration is to observe the correlation using different techniques. For instance, we are aiming to use mutual information, which is successfully applied in [ 25 ], to estimate the correlation between two cryptocurrencies. This method can overcome obstacles from popular linear and non-linear methods since it can measure the non-linear correlation while allowing the existence of non-monotonic relationships.…”

Biclustering high‐frequency financial time series based on information theory

“…We compute the MI between stock returns similar to Liu et al [39], by employing a jackknife version of the kernel estimate with equalized bandwidth varying over an interval [37]. The estimated MI is the largest value among these kernel estimates and its computation is summarized in the following steps.…”

The Linear Relationship Model with LASSO for Studying Stock Networks

“…We recently proposed to use mutual information to measure the nonlinear dependencies between stocks [ 21 , 22 ]. The information theory has been used recently to study stock relationship networks and other related financial problems [ 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. It is important to emphasize that the complexity of stock market systems may lead to a number of interactive patterns among stocks, and hence different measurements are needed to produce financial networks.…”