an:05554608
Zbl 1160.91396
Fortnow, Lance; Vohra, Rakesh V.
The complexity of forecast testing
EN
Econometrica 77, No. 1, 93-105 (2009).
0012-9682 1468-0262
2009
j
91B82 62M09 60G25 91A26 62G10 62P30
forecast testing; prediction; bounded rationality
Summary: 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.