Forecast Hedging and Calibration

TL;DR

This paper introduces the concept of forecast hedging to improve calibration in forecasting, providing new theoretical insights, improved definitions, and a simpler calibration procedure for binary events.

Contribution

It develops the theory of forecast hedging, differentiates between deterministic and stochastic calibration methods, and proposes a new, simpler calibrated forecasting procedure for binary events.

Findings

All calibration results can be derived using the forecast-hedging framework.

The paper introduces an improved definition of continuous calibration.

A new, simpler calibrated forecasting procedure for binary events is proposed.

Abstract

Calibration means that forecasts and average realized frequencies are close. We develop the concept of forecast hedging, which consists of choosing the forecasts so as to guarantee that the expected track record can only improve. This yields all the calibration results by the same simple basic argument while differentiating between them by the forecast-hedging tools used: deterministic and fixed point based versus stochastic and minimax based. Additional contributions are an improved definition of continuous calibration, ensuing game dynamics that yield Nash equilibria in the long run, and a new calibrated forecasting procedure for binary events that is simpler than all known such procedures.