PFCt

PFCt, short for Probabilistic Forecast Calibration over time, is a framework used to improve the reliability of probabilistic forecasts by explicitly accounting for temporal changes in forecast bias and dispersion. Unlike static calibration methods, PFCt treats calibration as a time-dependent process, allowing the relationship between forecast probabilities and observed outcomes to evolve with time.

The core idea of PFCt is to learn time-specific calibration mappings that adjust raw forecast probabilities to better reflect observed frequencies. This can be done by partitioning data into time segments (such as seasons, months, or rolling windows) or by modeling calibration as a smooth function of time. Calibration functions may be implemented with techniques such as isotonic regression, logistic regression, or nonparametric methods. The final calibrated forecast is obtained by applying the time-aware mapping to the original forecast probability.

Implementation considerations include data requirements, choice of temporal granularity, and methods to prevent overfitting. Adequate historical forecast–observation pairs are needed to train reliable time-dependent mappings, and regularization or cross-validation is often used to maintain generalization. Computational cost can be a factor when dealing with high-frequency data or many time segments. Validation typically involves reliability diagrams, Brier scores, and other forecast verification tools adapted to time-varying calibration.

Applications of PFCt span fields that rely on probabilistic forecasts, including weather and climate ensembles, hydrology, energy demand, and risk assessment in finance. By allowing calibration to adapt over time, PFCt aims to maintain forecast reliability in the presence of non-stationarity and evolving system dynamics.

See also: probabilistic forecasting, forecast calibration, reliability diagram, ensemble forecasting, non-stationarity.