Handbook of Exchange Rates

15.5 Model Uncertainty

Model uncertainty (or model risk) arises from the uncertainty over selecting a model specification. Consistent with our Bayesian approach, a natural criterion for resolving this uncertainty is to construct combined forecasts on the basis of posterior probability of each model. The posterior probability has three important advantages: (i) it is based on the marginal likelihood, and therefore accounts for parameter uncertainty,¹² (ii) it imposes a penalty for lack of parsimony (higher dimension), and (iii) it forms the basis of the BMA strategy discussed below. In computing the posterior probabilities, we set our prior belief to be that all models are equally likely.

We construct combined forecasts based on the BMA strategy and the Bayesian model winner (BMW) strategy (e.g., Geweke and Whiteman, 2006; and Timmermann, 2006). In assessing the economic value of combined forecasts, we treat the BMA and BMW strategies the same way as any of the individual models. For instance, we compute the performance fee and the break-even transaction cost for the BMA relative to the MLR benchmark. We apply BMA and BMW to three universes of models: (i) VOL is the universe of all nine univariate volatility specifications under the scalar DCC; (ii) CORR is the universe of the five multivariate correlation specifications (CCC, DCC, DCC_diag, ADCC, ADCC_diag) with GARCH volatility; and (iii) FULL is the complete universe of all 46 models, including the benchmark MLR.

15.5.1 The BMA ...