Bayesian Diagnostics in a Skew-Normal Autoregressive Model

Accepted - July 2025

Abstract

The autoregressive modeling is a crucial tool in time series analysis, finding extensive applications in various fields. This paper explores Bayesian statistical diagnostics for a skew-normal autoregressive model. Initially, a Markov Chain Monte Carlo algorithm, combining Gibbs sampling and Metropolis-Hastings, is utilized for parameter estimation of the model. Subsequently, different perturbation schemes are established for the priors, variances, and data, employing Bayesian factor, ϕ divergence, and posterior mean as measures of perturbation for Bayesian local influence analysis. Numerical simulations and comparative studies are conducted to demonstrate the effectiveness and superiority of the diagnostics. Finally, the diagnostic model is applied to empirical analysis of the daily log returns series of the Shanghai Composite Index in 2015.