Specification tests for non‐Gaussian maximum likelihood estimators

We propose generalized DWH specification tests which simultaneously compare three or more likelihood‐based estimators in multivariate conditionally heteroskedastic dynamic regression models. Our tests are useful for Garch models and in many empirically relevant macro and finance applications involving Var s and multivariate regressions. We determine the rank of the differences between the estimators' asymptotic covariance matrices under correct specification, and take into account that some parameters remain consistently estimated under distributional misspecification. We provide finite sample results through Monte Carlo simulations. Finally, we analyze a structural Var proposed to capture the relationship between macroeconomic and financial uncertainty and the business cycle. Durbin–Wu–Hausman tests partial adaptivity semiparametric estimators singular covariance matrices uncertainty and the business cycle C12 C14 C22 C32 C52