Consistent non-Gaussian pseudo maximum likelihood estimators

We characterise the mean and variance parameters that distributionally misspecified maximum likelihood estimators can consistently estimate in location-scale models, and provide simple closed-form consistent estimators for the rest. Including means and a multivariate coverage make our procedures useful for Garch-M models and empirically relevant macro and finance applications involving Vars and multivariate regressions. We study the statistical properties of our proposed consistent estimators, as well as their efficiency relative to Gaussian pseudo maximum likelihood and semiparametric procedures. We provide finite sample results through Monte Carlo simulations. Finally, we discuss two practical applications to individual stock returns and mean–variance efficiency/spanning tests.