Outlier detection and control in Bayesian vector autoregressive processes

Abstract

While outlier detection and control are not fundamental to the estimation of Bayesian Vector Autoregressive (BVAR) models, they represent a significant improvement that may enhance the robustness and reliability of estimation and forecasting. The increasing prevalence of big data pose challenges for monitoring and maintaining data quality for estimation. In this paper, the standard BVAR model is extended through Outlier Detection and Control (ODC), known as Extended BVAR-ODC model. The Extended BVAR-ODC decomposes the data generating process into three explicit components: a core VAR process with coefficient matrices and Gaussian innovations, an outlier component, and a multivariate normal-tempered innovation structure. Also, the ODC mechanism operates through a two-stage Bayesian procedure: posterior inference on outlier indicators, and simultaneous estimation of outlier impact coefficients and VAR parameters. It is shown in simulation that the Extended BVAR-ODC provides superior fit compared to the standard BVAR. Across all diagnostics, including parameter recovery, posterior trace convergence, mixing and predictive calibration, the Extended BVAR-ODC consistently outperforms the standard BVAR. Particularly, the posterior estimates of intercepts, lagged coefficients, and covariance matrices exhibit higher stability and smaller posterior dispersion. Additionally, residual analyses and goodness-of-fit confirm that the Extended BVAR-ODC effectively mitigates distortions induced by outliers. All performance measures favour the Extended BVAR-ODC, highlighting its superior generalization performance. Therefore, the Extended BVAR-ODC would be very useful in modeling financial systems that are subject to structural breaks or extreme events. Its outlier-induced specification ensures more robust inference under contaminated data distributions.