Inference in Misspecified GARCH‐M Models

The manuscript studies testing methods in systems with relationships between observed variables and conditional variances drawn from popular multivariate GARCH models. Although these methods have been extensively used to study the effects of uncertainty proxied by GARCH variables, inferential results are absent under misspecification or when using multi‐step estimators. Concentrating on test statistics for the hypothesis of no uncertainty impact, extensive Monte Carlo evidence is presented. Results show that severe size distortion and low power can occur when using two‐step procedures unless existing heteroskedasticity is modelled at every stage. In contrast, under moderate unconditional residual cross‐correlation, joint estimation of all model parameters yields test statistics with impressive relative power. In terms of misspecification, the consequences of ignoring asymmetries in the conditional variance matrix are shown to be potentially severe. Otherwise, estimation of DCC and diagonal BEKK models may be preferred relative to extended DCC and full BEKK counterparts, even under weak negative volatility spillovers. Issues are highlighted with an analysis of the relationships between production growth, inflation and their volatilities.