Statistical tests for equal predictive ability across multiple forecasting methods

We develop a multivariate generalization of the Giacomini-White tests for equal conditional predictive ability. The tests are applicable to a mixture of nested and non-nested models, incorporate estimation uncertainty explicitly, and allow for misspecification of the forecasting model as well as non-stationarity of the data. We introduce two finite-sample corrections, leading to good size and power properties. We also provide a two-step Model Confidence Set-type decision rule for ranking the forecasting methods into sets of indistinguishable conditional predictive ability, particularly suitable in dynamic forecast selection. In the empirical application we consider forecasting of the conditional variance of the S&P500 Index.