Robustness of canonical vector autoregressive representations under structural misspecification

Abstract

 This study evaluates the robustness and efficiency of canonical Vector Autoregressive (VAR) models relative to unrestricted VARmodels under correct specification and structural misspecification across different persistence regimes. Specifically, itinvestigates whether canonical VAR representations based on Kronecker index restrictions improve parameter estimation andforecasting in persistent multivariate systems. A Monte Carlo simulation framework was employed using VAR(1) processesgenerated under comfortably stable, moderately stable, and near-unit-root regimes. Sample sizes ranged from 10 to 720observations, while unrestricted VAR models were estimated using Generalized Least Squares (GLS) and Generalized Method ofMoments (GMM). Correctly specified and misspecified canonical VAR models were estimated under reduced canonical forms.Model performance was evaluated using the Frobenius norm, relative efficiency, Root Mean Square Error (RMSE), MeanAbsolute Error (MAE), and bias–variance decomposition across 500 simulation replications. The findings show that canonicalVAR models substantially improve parameter estimation, reducing estimation errors by approximately 75–85%, particularly insmall samples and highly persistent systems. Relative efficiency remained above two under near-unit-root dynamics, while evenmisspecified canonical models frequently outperformed unrestricted VAR models because variance reduction outweighedstructural bias. However, these estimation gains produced only marginal improvements in one-step-ahead forecast accuracy,indicating that forecast performance is primarily driven by innovation variance. Overall, canonical VAR models provide aparsimonious and statistically efficient alternative to unrestricted VAR models for parameter estimation, especially underpersistent dynamics, although their forecasting advantage is limited.