We propose new approaches to test for spanning in the return and stochastic discount factor mean-variance frontiers, which assess if either the centred or uncentred mean and cost representing portfolios are shared by the initial and extended sets of assets. We show that our proposed tests are...

We rank the efficiency of several likelihood-based parametric and semiparametric estimators of conditional mean and variance parameters in multivariate dynamic models with i.i.d. spherical innovations, and show that Gaussian pseudo maximum likelihood estimators are inefficient except under...

We derive indirect estimators of multivariate conditionally heteroskedastic factor models in which the volatilities of the latent factors depend on their past values. Specifically, we calibrate the analytical score of a Kalman-filter approximation, taking into account the inequality constraints...