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Forecasts are useless whenever the forecast error variance fails to
be smaller than the unconditional variance of the target variable. This paper
proposes tests for the null hypothesis that forecasts become uninformative
beyond some limiting forecast horizon h*. Following Diebold and
Mariano (DM, 1995) we propose a test based on the comparison of the
mean-squared error of the forecast and the sample variance. We show that the
resulting test does not possess a normal limiting distribution and suggest two
simple modifications of the DM-type test with different limiting null
distributions. Furthermore, a forecast encompassing test is developed that
tends to better control the size of the test. In our empirical analysis, we
apply our tests to macroeconomic forecasts from the survey of Consensus
Economics. Our results suggest that forecasts of macroeconomic key variables
are barely informative beyond 2--4 quarters ahead.
