Multivariate Control Charts and Changepoint Detection for Multivariate Functional Data by Nonparametric Conditional Distribution and FPCA

ABSTRACT

Detecting structural changes in multivariate functional data is difficult when strong dependence and non‐linear relationships obscure persistent shifts. Existing statistical process control and multivariate functional monitoring methods often lose power in such settings due to variance inflation induced by cross‐correlation. This study focuses on improving practical changepoint detection through dependence‐aware preprocessing within a functional monitoring framework. We propose a change point detection method that integrates nonparametric conditional distribution transformations with functional principal component analysis (FPCA). The conditional transformation reduces inter‐variable dependence by standardizing each functional component relative to its conditional distribution, allowing localized dependence changes to emerge more clearly after common variation is removed. FPCA then captures dominant temporal variation, enabling sustained mean and variance shifts to be detected through low‐dimensional score processes. Method effectiveness is assessed through simulation studies with controlled change points under varying dependence structures. Performance is evaluated using detection delay, false alarm rates, and localization accuracy, and compared against established multivariate functional monitoring methods without conditional preprocessing. Both simulations and financial applications show that the conditional framework detects structural shifts missed by conventional marginal monitoring approaches, particularly in strongly correlated environments. The proposed approach consistently achieves faster detection and improved stability in highly dependent settings. An application to high‐frequency financial index data further demonstrates that the framework can identify stock‐specific regime changes obscured by broader market movements.