Research supported in part by NSF grant ITR IIS-0121678. We thank A. Sandroni and W. Olszewski and the referees for useful comments.
The Complexity of Forecast Testing
Article first published online: 15 DEC 2008
© 2009 The Econometric Society
Volume 77, Issue 1, pages 93–105, January 2009
How to Cite
Fortnow, L. and Vohra, R. V. (2009), The Complexity of Forecast Testing. Econometrica, 77: 93–105. doi: 10.3982/ECTA7163
- Issue published online: 15 DEC 2008
- Article first published online: 15 DEC 2008
- Manuscript received May, 2007; final revision received June, 2008.
- Forecast testing;
- bounded rationality
Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear-time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature.