Do we need non-linear models to predict REIT returns?

We investigate whether the favorable performance of a fairly simple multistate multivariate Markov regime switching model relative to even very complex multivariate GARCH specifications, recently reported in the literature using measures of in-sample prediction accuracy, extends to pseudo out-of-sample forecasting accuracy. We recursively estimate the parameters of each model specification and use it to forecast returns and variances for the REIT, stock, and bond asset classes; REIT-stock, REIT-bond, and stock-bond covariances; and the entire return densities for the three assets. Out-of-sample forecast tests indicate that the four-regime MS model is, indeed, superior to all of the GARCH specifications in forecasting returns in each asset class, but is inferior in forecasting return variances. For the purpose of forecasting inter-asset return covariances, however, the MS model is surprisingly superior to all of the GARCH models.