How far can we forecast?

Forecasts are useless whenever the forecast error variance fails to be smaller than
the unconditional variance of the target variable. This paper develops 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 limiting normal 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.