Model confidence sets for forecasting models

The paper introduces the model confidence set (MCS) and applies it to the selection of forecasting models. An MCS is a set of models that is constructed so that it will contain the "best" forecasting model, given a level of confidence. Thus, an MCS is analogous to a confidence interval for a parameter. The MCS acknowledges the limitations of the data so that uninformative data yield an MCS with many models, whereas informative data yield an MCS with only a few models. We revisit the empirical application in Stock and Watson (1999) and apply the MCS procedure to their set of inflation forecasts. In the first pre-1984 subsample we obtain an MCS that contains only a few models, notably versions of the Solow-Gordon Phillips curve. On the other hand, the second post-1984 subsample contains little information and results in a large MCS. Yet, the random walk forecast is not contained in the MCS for either of the samples. This outcome shows that the random walk forecast is inferior to inflation forecasts based on Phillips curve-like relationships.