Detecting long-lived autodependency changes in a multivariate system via change point detection and regime switching models

Abstract

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.

A complex systems approach to the study of change in psychotherapy

“…His mood ratings showed indicators of critical slowing (increased temporal autocorrelations, increased variance, and stronger intercorrelations) before the onset of the depressive episode. This pattern of findings held consistent in subsequent re-analyses of the same data with more sophisticated tests of correlational change in longitudinal data [ 105 , 106 ]. Early warning sign toolboxes are available for detecting signals of critical slowing in R statistical package [ 107 , 108 ], and a number of studies are currently underway.…”

“…Methodologists have developed ways to examine networks in windows of relative stability, such as the beginning and end of treatment [121], and to include intervention as a variable in network models to examine treatment effects on symptoms at different time windows [122]. More recently, analytic strategies are being developed to examine nonlinear jumps and regime (attractor) changes using network analyses [105,123]. Tschacher and Haken [15] describe methods from dynamical systems science and synergetics to examine effects over time of one component in a system on another component, using nonlinear differential equations.…”

Temporal evolution of IP25 and other highly branched isoprenoid lipids in sea ice and the underlying water column during an Arctic melting season

“…Correlation change-point analyses (Cabrieto et al, 2017;Cabrieto et al, 2018) were carried out using a cp3o (change points via probabilistically pruned objective; James and Matteson, 2015) test to identify the approximate timing of significant correlation shifts between variables in SPM samples along the sampling interval. Pearson's correlation with a sampling window of 11 was run using the productmoment correlation coefficient (r), as a measure of association between variables and correlation significance determined at p ≤ 0.05.…”

Identifying Qualitative Between-Subject and Within-Subject Variability: A Method for Clustering Regime-Switching Dynamics

“…Besides, we need to compare the mixRHLP modeling approach to other model-based and datadriven approaches for clustering regime-switching dynamics in simulations and applications. Candidate approaches include but not limited to the mixture of hidden Markov models (Chamroukhi and Nguyen, 2019) and potential extensions of existing data-driven methods that identify clusters or regimes (e.g., Cabrieto et al, 2018). Moreover, it is worthwhile to examine different imputation methods for missing data, for example, the newly developed ones that depend on machine learning approaches (Yoon et al, 2018).…”