## Abstract

Each period an outcome (out of finitely many possibilities) is observed. For simplicity assume two possible outcomes, a and b. Each period, a forecaster announces the probability of a occurring next period based on the past Consider an arbitrary subsequence of periods (e.g., odd periods, even periods, all periods in which b is observed, etc.). Given an integer n, divide any such subsequence into associated sub-subsequences in which the forecast for a is between (i/n, i + 1/n), i ∈ {0, 1,...,n}. We compare the forecasts and the outcomes (realized next period) separately in each of these subsubsequences. Given any countable partition of [0,1] and any countable collection of subsequences, we construct a forecasting scheme such that for all infinite strings of data, the long-run average forecast for a matches the long-run frequency of realized a's.

Original language | English (US) |
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Pages (from-to) | 141-153 |

Number of pages | 13 |

Journal | Mathematics of Operations Research |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2003 |

## Keywords

- Calibration
- Forecast
- Probabilistic forecast

## ASJC Scopus subject areas

- General Mathematics
- Computer Science Applications
- Management Science and Operations Research