This paper proposes a class of models that jointly model returns and ex post variance measures under a Markov switching framework. Both univariate and multivariate return versions of the model are introduced. Estimation can be conducted under a fixed dimension state space or an infinite one. The proposed models can be seen as nonlinear common factor models subject to Markov switching and are able to exploit the information content in both returns and ex post volatility measures. Applications to equity returns compare the proposed models to existing alternatives. The empirical results show that the joint models improve density forecasts for returns and point predictions of return variance. Using the information in ex post volatility measures can increase the precision of parameter estimates, sharpen the inference on the latent state variable, and improve portfolio decisions.
