A general approach for Bayesian case influence analysis in GARCH models

This paper proposes a Bayesian diagnostic framework for assessing case influence in Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models. By leveraging the exact analytical formulation of the ϕ-divergence family via Markov Chain Monte Carlo (MCMC) integration. We introduce a novel Dirichlet prior specification that natively enforces the strict covariance stationarity constraint of the GARCH(p,q) model. Furthermore, we develop a dynamic, probabilistically interpretable threshold calibration based on Generalized Extreme Value Distribution (GEVD) quantile regression. Simulation studies demonstrate that this dynamic calibration actively adjusts to the conditional variance to strictly bound the empirical family-wise Type I error rate, isolating influential observations unexplained by the GARCH dynamics from smaller perturbations. The practical utility of the framework is demonstrated through applications to the NYSE composite index and Yihai Kerry Arawana Holdings.