Comparing forecasts of inflation using time distance

When considering the relative quality of forecasts the method of comparison is relevant: should we use vertical measures, such as mean square forecasting error, or the recently developed horizontal measure time distance? Four models for inflation in the US are considered based on univariate time series, a leading indicator, a univariate model combining with the specifications of the two models, and a bivariate model. According to the mean squared forecast errors an AR(1) model is superior, but it performs much less well than models using a leading indicator when considered in terms of time distance. These results hold for both standard procedures and for the bootstrap reality check.