The Complexity of Forecast Testing

2009 Econometrica  
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 (2003) shows that any test which passes a forecaster who knows the distribution of nature, can 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 a distribution
more » ... of nature such that any forecaster without knowledge of the future that can fool the test must be able to solve PSPACE-hard problems by requiring the forecaster to simulate a prover in an arbitrary interactive proof system.
doi:10.3982/ecta7163 fatcat:ignd4cxs5jbqvj7qvouj2qt4ka