A PREQUENTIAL TEST FOR EXCHANGEABLE THEORIES ALVARO SANDRONI AND ERAN SHMAYA Abstract. We construct a prequential test of probabilistic forecasts that does not reject correct forecasts when the data-generating processes is exchangeable and is not manipulable by a false forecaster. A potential expert, named Bob, claims that he is informed about which stochastic process will generate the future data. A tester, named Alice, does not know whether Bob does, in fact, know anything relevant about the process (i.e., something Alice does not know). However, Bob will repeatedly announce a forecast of next period’s outcomes. A basic question is whether Alice can eventually determine whether Bob is informed. A growing literature answers this question in the negative (see Olszewski (2011) for a literature review). A prequential test takes, as input, Bob’s forecasts and realized outcomes and returns, as output, a reject or pass verdict. Sandroni (2003) shows that if a perfectly informed expert (i.e., predicts according to the data generating process) is likely to pass Alice’s test then a completely uninformed expert (i.e., knows nothing about the data generating process) can strategically concoct forecasts that are likely to pass the test, regardless of the realized outcomes. Thus, Alice’s test cannot screen informed and uninformed, but strategic, experts. Olszewski and Sandroni (2008) extended this result to finite, possibly unbounded horizon. There are no clear benefits of running a test if it is known, at the outset, that it will return a pass verdict. So, the results in this literature cast doubt on the use of empirical tests when experts are potentially strategic. However, two key assumptions underlying the impossibility 2000 Mathematics Subject Classification. Primary: 62A01. Secondary: 91A40. 1 arXiv:1305.4421v1 [math.ST] 20 May 2013 1. Introduction