Dating multiple change points in the correlation matrix

Abstract

We propose a nonparametric procedure for detecting and dating multiple change points in the correlation matrix of a sequence of random variables. The procedure is based on a test for changes in correlation matrices at an unknown point in time recently proposed by Wied (2014). Although the procedure requires constant expectations and variances, only mild assumptions on the serial dependence structure are assumed. We show the validity of the procedure including the convergence rate of the change point estimators. Moreover, we illustrate its performance in finite samples by means of a simulation study and the analysis of a real data example with financial returns. These examples show that the proposed algorithm has large power in finite samples.

: An R Package for performing kernel change point detection on the running statistics of multivariate time series

“…Therefore, the signal may not be large enough to detect it. Indeed, neither the general purpose method E-divisive (Matteson & James, 2014) nor correlation specific methods such as Frobenius norm (Barnett & Onnela, 2016) or CUSUM (Galeano & Wied, 2017) were able to detect the change points, whereas KCP-RS on the running correlations was (see https://osf.io/zrh4v/ for R code and output of the E-divisive method. Code for the other methods is available upon request).…”

“…For instance, at the onset of physically (De Roover et al, 2014), mentally (Barnett & Onnela, 2016;Grassmann et al, 2016) or emotionally (Bulteel et al, 2014) demanding events, human physiology exhibits such sudden changes. Also nonhuman complex systems can show similar abrupt changes in reaction to critical events, such as computer network attacks (Tartakovsky et al, 2006), geological disasters such as volcanic eruptions (Tárraga et al, 2014), epidemic breakouts (Texier et al, 2016), and financial crises (Galeano & Wied, 2017).…”

“…Change point detection methods were developed to retrospectively capture such sudden changes in statistical features (Brodsky & Darkhovsky, 1993;Chen & Gupta, 2012). These methods are employed to address two crucial questions (Bulteel et al, 2014;Cabrieto et al, 2019;De Roover et al, 2014;Galeano & Wied, 2017) that researchers have. The first question pertains to the exact timing of the changes and how proximal they are to the onset of an event if this is known.…”

“…A number of methods and software packages have been proposed to aid researchers in capturing and characterizing unknown changes in time series data. However, they often fall short in practice because they are restricted to univariate data (Erdman & Emerson, 2007;Killick & Eckley, 2014;Ross, 2015) restricted to a specific statistic or statistical model (Barnett & Onnela, 2016;Dürre et al, 2015;Galeano & Wied, 2017;Zeileis et al, 2002) or impose other stringent assumptions on the data (Chen & Gupta, 2012;Davis et al, 2006;Lavielle, 2005). There are multivariate, non-parametric methods available (Arlot, Celisse, & Harchaoui, 2012;Bulteel et al, 2014;Lung-Yut-Fong, Lévy-Leduc, & Cappé, 2012;Matteson & James, 2014) that can potentially detect all types of changes, but they often lack power to detect changes in statistics that do not pertain to the mean level (e.g., correlation ;Cabrieto, Tuerlinckx, Kuppens, Wilhelm, et al, 2018) and do not uncover which statistics are exactly involved in the change.…”

Robust multiple change-point detection for multivariate variability using data depth

“…Wied et al (2012) proposed a nonparametric approach based on cumulative sums of sample correlation coefficients to detect a single change-point in the correlation structure of bivariate observations. This was later extended to multiple change-points (Galeano and Wied, 2014) and further to the multivariate setting (Galeano and Wied, 2017). Posch et al (2019) has further extended the methods of (Galeano and Wied, 2017) to the high-dimensional setting by first applying dimension reduction techniques.…”