Diagnostic analystics in the Bayesian vector autoregressive model

The vector autoregressive model is extensively employed in macroeconomics, finance, and the natural sciences. However, it often encounters the issue of over-parametrization, resulting in undesirable behavior within the model. In this paper, we utilize the Bayesian vector autoregressive model as a tool to tackle this problem. Additionally, we employ the Bayesian local influence method to detect possible extreme observations under the model. We use posterior inference to estimate related parameters and construct Bayesian perturbation schemes for priors, variance, and data perturbations. Bayesian local influence is conducted based on three objective functions: Bayes factor, ϕ divergence, and posterior mean. To demonstrate the effectiveness of the diagnostics, we conduct numerical simulations. In the real data example, we use US inflation, unemployment, and interest rate data to verify this method's effectiveness.