Calibrated Forecasting and Merging

Abstract

Consider a finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subjective probabilities to future states. The resulting subjective forecast merges to the objective distribution if, with time, the forecasted probabilities converge to the correct (but unknown) probabilities. The forecast is calibrated if observed long-run empirical distributions coincide with the forecasted probabilities. This paper links unobserved reliability of forecasts to their observed empirical performance by demonstrating full equivalence between notions of merging and of calibration, and discusses implications of this equivalence for the literature of forecasting and learning. Journal of Economic Literature Classification Numbers: C5, C11, C73, D83.