Theoretical guidelines for a partially informed forecast examiner

The paper explores probability theory foundations behind evaluation of probabilistic forecasts. The emphasis is on a situation when the forecast examiner possesses only partially the information which was available and was used to produce a forecast. We argue that in such a situation forecasts should be judged by their conditional auto-calibration. Necessary and sufficient conditions of auto-calibration are discussed and expressed in the form of testable moment conditions. The paper also analyzes relationships between forecast calibration and forecast efficiency.