Forecasting intra-day volatility by vine copula regression using MFPCA and lagged covariates for high-frequency financial time series

This research develops a vine copula regression framework for predicting intra-day volatility using multivariate high-frequency time series. The model incorporates lagged covariates and eigenfunctions obtained from multivariate functional principal component analysis (MFPCA). The MFPCA eigenfunctions capture hidden dependence structures and explain major variations in multivariate functional data, while vine copula regression provides a flexible, non-linear, and distribution-free tool for modeling highly correlated and non-normal covariates. To demonstrate the effectiveness of the proposed method, we analyze intra-day volatilities of the Korea Composite Stock Price Index based on 1-min log-return data, with covariates from Samsung Electronics, SK Hynix, and Hyundai Motor. In addition, we introduce a vine copula regression residual control chart that integrates MFPCA eigenfunctions and lagged covariates, enabling the detection of outliers and structural changes in functional time series. The real data application highlights the practical utility of the proposed approach for volatility forecasting and monitoring.