Bayesian case influence analysis for GARCH models based on Kullback–Leibler divergence

Abstract

Influence analysis has become an important tool for statistical analysis. This paper is concerned with Bayesian case influence analysis for generalized autoregressive conditional heteroscedasticity (GARCH) model. Case influence analysis is developed for both the joint and marginal posterior distributions based on the Kullback–Leibler divergence (K–L divergence). A simplified expression is presented for computing the K–L divergence between the full data posterior distribution and the case-deleted posterior distributions. The related computations can be done numerically by Markov Chain Monte Carlo samples from posterior distribution with full data. Some simulation studies are carried out to examine the performance of the proposed methods and show the relations between case-deletion model (CDM) and mean-shift outlier model (MSOM) for the GARCH models. Meanwhile, the methods are also illustrated by a real data.