📈 Forecast Error

Forecast Error#

The difference between a forecast and the realised value.

Important

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What it is#

Forecast error is the gap between what happened and what was predicted — the residual

\[e_t = y_t - \hat{y}_t.\]

A single error means little; forecast quality is summarized by aggregating errors into metrics.

Common metrics#

MAE \(= \frac{1}{N}\sum_t |y_t - \hat{y}_t|\) is robust and interpretable, and the forecast that minimizes it is the median. RMSE \(= \sqrt{\frac{1}{N}\sum_t (y_t - \hat{y}_t)^2}\) penalizes large misses more and is minimized by the mean, but is harder to read. MAPE (mean absolute percentage error) is scale-free but explodes when actuals are near zero; sMAPE is a bounded symmetric variant, still shaky near zero. MASE scales MAE by a naive forecast’s error, making it scale-free and interpretable (\(<1\) beats naive).

Use several#

No single metric tells the whole story — MAPE can look great while bias quietly builds, and MAE can hide a few enormous misses — so report several: an absolute metric (MAE / RMSE), a scaled one (MASE), and a bias measure.

Theme: Signal Processing & Time Series · All terminology

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Mind map — connected ideas

Naïve Baseline Forecast · Point Forecasts · Forecasting Benchmarks · Average Absolute Error (AAE) · Time Series Forecasting · Relative accuracy

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More in Signal Processing & Time Series

ARIMA (AutoRegressive Integrated Moving Average) · Bayesian Time Series · Forecasting Benchmarks · Forecasting Competitions · Log-Space · Low-pass Filtering · LSTM — Long Short-Term Memory Networks · M-Competitions (Makridakis Competitions) · Naïve Baseline Forecast · Prophet — Time Series Forecasting by Facebook (Meta) · Seasonal Lag · Seasonality · Signal Processing · Simple Baseline Methods