Uncovering the dynamics of correlation structures relative to the collective market motion

Abstract

The measured correlations of financial time series in subsequent epochs change considerably as a function of time. When studying the whole correlation matrices, quasi-stationary patterns, referred to as market states, are seen by applying clustering methods. They emerge, disappear or reemerge, but they are dominated by the collective motion of all stocks. In the jargon, one speaks of the market motion, it is always associated with the largest eigenvalue of the correlation matrices. Thus the question arises, if one can extract more refined information on the system by subtracting the dominating market motion in a proper way. To this end we introduce a new approach by clustering reduced-rank correlation matrices which are obtained by subtracting the dyadic matrix belonging to the largest eigenvalue from the standard correlation matrices. We analyze daily data of 262 companies of the S&P 500 index over a period of almost 15 years from 2002 to 2016. The resulting dynamics is remarkably different, and the corresponding market states are quasi-stationary over a long period of time. Our approach adds to the attempts to separate endogenous from exogenous effects.

Non-stationarity in correlation matrices for wind turbine SCADA-data and implications for failure detection

“…This is slightly different from the approach used in former works by Münnix et al (2012, Stepanov et al (2015) and Heckens et al (2020), where a threshold is introduced and all clusters are bisected until no single existing cluster has an average internal distance larger than the threshold. However, the threshold is then set based on the number of clusters wanted.…”

“…Such compromises are common when dealing with correlation matrix time series (Marti et al, 2021;Heckens et al, 2020).…”

“…We choose the bisecting k-means algorithm to perform our clustering (Steinbach et al, 2000;Tan et al, 2019). This is the algorithm that was also used to determine states in the financial markets by Münnix et al (2012) and Heckens et al (2020). It can be described as a hybrid of standard k-means clustering (Lloyd, 1982;Jain, 2010) and hierarchical clustering (Kaufman and Rousseeuw, 1990).…”

Comment on wes-2021-107

“…Any method separating objects into groups needs a distance measure defined between those objects. For the correlation matrices we choose the euclidean distance (Heckens et al, 2020). The reader can imagine that all matrix entries are written into a vector, effectively arranging the columns of the matrix underneath each other, so that the standard euclidean distance between vectors can be applied.…”

Network geometry and market instability

“…To understand the topology of the correlation-based networks as well as to define the complexity, a volume-based dimension has also been proposed by Nie et al [32]. There have also been some novel studies where the financial market has been considered as a quasistationary system, and then the ensuing dynamics have been studied [33][34][35][36][37].…”