QuanTAlib/lib/errors/_index.md

Errors

"All models are wrong. Error metrics tell you how wrong." Adapted from George Box

Error metrics and loss functions for model/strategy evaluation. All error indicators accept two input series (actual and predicted values) and compute rolling error metrics over a configurable period.

Indicators

Indicator	Full Name	Description
HUBER	Huber Loss	Combines MSE and MAE. Configurable outlier threshold δ.
LOGCOSH	Log-Cosh Loss	Smooth approximation to MAE. Twice-differentiable.
MAE	Mean Absolute Error	Average of absolute differences. Robust baseline.
MAAPE	Mean Arctangent APE	Bounded percentage error using arctangent. Range: 0 to π/2.
MAPD	Mean Absolute % Deviation	Percentage error relative to mean of actual and predicted.
MAPE	Mean Absolute % Error	Percentage error relative to actual. Unbounded when actual≈0.
MASE	Mean Absolute Scaled Error	Scale-free. Uses naive forecast as baseline.
MDAE	Median Absolute Error	Median of absolute differences. Outlier-robust. O(n log n).
MDAPE	Median Absolute % Error	Median percentage error. Outlier-robust. O(n log n).
ME	Mean Error	Signed average. Detects systematic bias.
MPE	Mean Percentage Error	Signed percentage. Shows directional bias.
MRAE	Mean Relative Absolute Error	Error relative to naive forecast.
MSE	Mean Squared Error	Squared differences. Penalizes large errors heavily.
MSLE	Mean Squared Log Error	MSE on log-transformed values. For multiplicative errors.
PSEUDOHUBER	Pseudo-Huber Loss	Smooth Huber approximation. Fully differentiable.
QUANTILE	Quantile Loss	Asymmetric loss for quantile regression. Pinball loss.
RAE	Relative Absolute Error	Absolute error relative to mean predictor.
RMSE	Root Mean Squared Error	√MSE. Same units as input. Penalizes outliers.
RMSLE	Root Mean Squared Log Error	√MSLE. For multiplicative error structures.
RSE	Relative Squared Error	Squared error relative to mean predictor.
RSQUARED	R² (Coefficient of Determination)	Variance explained. 1 = perfect. Can be negative.
SMAPE	Symmetric MAPE	Bounded 0-200%. Symmetric around zero.
THEILU	Theil's U Statistic	Forecast vs naive. <1 beats naive. >1 worse than naive.
TUKEY	Tukey Biweight Loss	Hard-rejects outliers beyond threshold. Redescending.
WMAPE	Weighted MAPE	Volume-weighted percentage error. For heterogeneous data.
WRMSE	Weighted RMSE	Weighted root mean squared error. Custom observation weighting.