Forecasterror

Forecasterror is the discrepancy between a forecasted value and the actual observed outcome. It is used as a generic label for forecast errors across disciplines such as meteorology, economics, and epidemiology. For a forecast ŷ_t of an observation y_t at time t, the forecast error is commonly defined as e_t = y_t − ŷ_t, though conventions vary.

Sign conventions vary: some communities define e_t = ŷ_t − y_t. The sign chosen affects the interpretation of bias, which is the average of forecast errors and indicates whether forecasts tend to over- or under-predict on average.

To summarize forecasterror, common metrics include mean absolute error (MAE), root-mean-square error (RMSE), and mean absolute percentage error (MAPE). For probabilistic forecasts, proper scoring rules such as the continuous ranked probability score (CRPS) are used; forecast skill is often assessed relative to a reference forecast.

Forecasterror informs model validation, calibration, and selective improvement. It can be decomposed into systematic bias and random error; addressing bias and model error can reduce forecasterror. Limitations include sensitivity to outliers, data quality, and nonstationarity in the underlying process.

See also: Forecasting, Forecast bias, RMSE, MAE, MAPE, Calibration.