Detecting abrupt correlation changes in multivariate time series is crucial in many application fields such as signal processing, functional neuroimaging, climate studies, and financial analysis. To detect such changes, several promising correlation change tests exist, but they may suffer from severe loss of power when there is actually more than one change point underlying the data. To deal with this drawback, we propose a permutation based significance test for Kernel Change Point (KCP) detection on the running correlations. Given a requested number of change points K, KCP divides the time series into K + 1 phases by minimizing the within-phase variance. The new permutation test looks at how the average within-phase variance decreases when K increases and compares this to the results for permuted data. The results of an extensive simulation study and applications to several real data sets show that, depending on the setting, the new test performs either at par or better than the state-of-the art significance tests for detecting the presence of correlation changes, implying that its use can be generally recommended.

Change point detection in multivariate time series is a complex task since next to the mean, the correlation structure of the monitored variables may also alter when change occurs. DeCon was recently developed to detect such changes in mean and\or correlation by combining a moving windows approach and robust PCA. However, in the literature, several other methods have been proposed that employ other non-parametric tools: E-divisive, Multirank, and KCP. Since these methods use different statistical approaches, two issues need to be tackled. First, applied researchers may find it hard to appraise the differences between the methods. Second, a direct comparison of the relative performance of all these methods for capturing change points signaling correlation changes is still lacking. Therefore, we present the basic principles behind DeCon, E-divisive, Multirank, and KCP and the corresponding algorithms, to make them more accessible to readers. We further compared their performance through extensive simulations using the settings of Bulteel et al. (Biological Psychology, 98 (1), 29-42, 2014) implying changes in mean and in correlation structure and those of Matteson and James (Journal of the American Statistical Association, 109 (505), 334-345, 2014) implying different numbers of (noise) variables. KCP emerged as the best method in almost all settings. However, in case of more than two noise variables, only DeCon performed adequately in detecting correlation changes.

Long-lived simultaneous changes in the autodependency of dynamic system variables characterize crucial events as epileptic seizures and volcanic eruptions and are expected to precede psychiatric conditions. To understand and predict such phenomena, methods are needed that detect such changes in multivariate time series. We put forward two methods: First, we propose KCP-AR, a novel adaptation of the general-purpose KCP (Kernel Change Point) method. Whereas KCP is implemented on the raw data and does not shed light on which parameter changed, KCP-AR is applied to the running autocorrelations, allowing to focus on changes in this parameter. Second, we revisit the regime switching AR(1) approach and propose to fit models wherein only the parameters capturing autodependency differ across the regimes. We perform a simulation study comparing both methods: KCP-AR outperforms regime switching AR(1) when variables are uncorrelated, while the latter is more reliable when multicolinearity is severe. Regime switching AR(1), however, may yield recurrent switches even when the change is long-lived. We discuss an application to psychopathology data where we investigate whether emotional inertia -the autodependency of affective states- changes before a relapse into depression.

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