Equal predictability test for multi-step-ahead system forecasts invariant to linear transformations

The paper derives a test for equal predictability of multi-step-ahead system forecasts that is invariant to linear transformations. The test is a multivariate version of the Diebold-Mariano test. An invariant metric for multi-step-ahead system forecasts is necessary as the conclusions otherwise can depend on how the forecasts are reported (e.g., as in levels or differences; or log-levels or growth rates). The test is used in comparing quarterly multi-step-ahead system forecasts made by Statistics Norway with similar forecasts made by Norges Bank.