Vine copula MFPCA residual control chart for sparse multivariate functional data

We introduce a multivariate functional principal component analysis (MFPCA) residual control chart for multivariate functional data. Our method utilizes the vine copula technique and is applied to high-frequency financial data. We employ functional eigenfunctions to uncover hidden dependence structures and explain variations in sparse multivariate longitudinal data through MFPCA. With these functional eigenfunctions, we create a vine copula-based residual control chart for sparse multivariate longitudinal data. To handle sparse multivariate longitudinal data in this context, we employ predictive mean matching imputation. As part of real-world applications, we conduct analysis on high-frequency time series data for five technology stocks listed on the Nasdaq exchange, as well as high-frequency air quality data obtained from a significantly polluted area within an Italian city.