Testing for the Presence of Correlation Changes in a Multivariate Time Series: A Permutation Based Approach

Area of Science:

• Multivariate time series analysis
• Statistical signal processing
• Data mining and pattern recognition

Background:

• Detecting abrupt changes in correlations within multivariate time series is vital across diverse fields like finance, climate science, and neuroimaging.
• Existing methods often lack power when multiple correlation change points are present, leading to missed or inaccurate detection.

Purpose of the Study:

• To develop a robust permutation-based significance test for Kernel Change Point (KCP) detection capable of identifying multiple underlying correlation changes.
• To address the power limitations of current tests when dealing with complex, multi-change point scenarios in time series data.

Main Methods:

• Proposed a novel permutation test integrated with Kernel Change Point (KCP) detection for analyzing running correlations in multivariate time series.
• KCP algorithm segments the time series into K+1 phases by minimizing intra-phase variance for a given number of change points (K).
• The significance test evaluates the reduction in average within-phase variance as K increases, comparing it against permuted data distributions.

Main Results:

• Extensive simulations and real-world data applications demonstrated the efficacy of the proposed permutation test.
• The new method performs comparably to or better than state-of-the-art significance tests for detecting correlation changes, especially in multi-change point scenarios.
• The test effectively identifies the presence of correlation changes, offering improved sensitivity over existing approaches.

Conclusions:

• The developed permutation-based KCP significance test offers a powerful and reliable tool for detecting abrupt correlation changes in multivariate time series.
• Its ability to handle multiple change points makes it a valuable advancement over existing methods.
• The general applicability and strong performance suggest this method can be widely recommended for relevant analytical tasks.