# 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](lib/errors/huber/Huber.md) | Huber Loss | Combines MSE and MAE. Configurable outlier threshold δ. |
| [LOGCOSH](lib/errors/logcosh/Logcosh.md) | Log-Cosh Loss | Smooth approximation to MAE. Twice-differentiable. |
| [MAE](lib/errors/mae/Mae.md) | Mean Absolute Error | Average of absolute differences. Robust baseline. |
| [MAAPE](lib/errors/maape/Maape.md) | Mean Arctangent APE | Bounded percentage error using arctangent. Range: 0 to π/2. |
| [MAPD](lib/errors/mapd/Mapd.md) | Mean Absolute % Deviation | Percentage error relative to mean of actual and predicted. |
| [MAPE](lib/errors/mape/Mape.md) | Mean Absolute % Error | Percentage error relative to actual. Unbounded when actual≈0. |
| [MASE](lib/errors/mase/Mase.md) | Mean Absolute Scaled Error | Scale-free. Uses naive forecast as baseline. |
| [MDAE](lib/errors/mdae/Mdae.md) | Median Absolute Error | Median of absolute differences. Outlier-robust. O(n log n). |
| [MDAPE](lib/errors/mdape/Mdape.md) | Median Absolute % Error | Median percentage error. Outlier-robust. O(n log n). |
| [ME](lib/errors/me/Me.md) | Mean Error | Signed average. Detects systematic bias. |
| [MPE](lib/errors/mpe/Mpe.md) | Mean Percentage Error | Signed percentage. Shows directional bias. |
| [MRAE](lib/errors/mrae/Mrae.md) | Mean Relative Absolute Error | Error relative to naive forecast. |
| [MSE](lib/errors/mse/Mse.md) | Mean Squared Error | Squared differences. Penalizes large errors heavily. |
| [MSLE](lib/errors/msle/Msle.md) | Mean Squared Log Error | MSE on log-transformed values. For multiplicative errors. |
| [PSEUDOHUBER](lib/errors/pseudohuber/Pseudohuber.md) | Pseudo-Huber Loss | Smooth Huber approximation. Fully differentiable. |
| [QUANTILE](lib/errors/quantile/Quantile.md) | Quantile Loss | Asymmetric loss for quantile regression. Pinball loss. |
| [RAE](lib/errors/rae/Rae.md) | Relative Absolute Error | Absolute error relative to mean predictor. |
| [RMSE](lib/errors/rmse/Rmse.md) | Root Mean Squared Error | √MSE. Same units as input. Penalizes outliers. |
| [RMSLE](lib/errors/rmsle/Rmsle.md) | Root Mean Squared Log Error | √MSLE. For multiplicative error structures. |
| [RSE](lib/errors/rse/Rse.md) | Relative Squared Error | Squared error relative to mean predictor. |
| [RSQUARED](lib/errors/rsquared/Rsquared.md) | R² (Coefficient of Determination) | Variance explained. 1 = perfect. Can be negative. |
| [SMAPE](lib/errors/smape/Smape.md) | Symmetric MAPE | Bounded 0-200%. Symmetric around zero. |
| [THEILU](lib/errors/theilu/Theilu.md) | Theil's U Statistic | Forecast vs naive. <1 beats naive. >1 worse than naive. |
| [TUKEY](lib/errors/tukey/Tukey.md) | Tukey Biweight Loss | Hard-rejects outliers beyond threshold. Redescending. |
| [WMAPE](lib/errors/wmape/Wmape.md) | Weighted MAPE | Volume-weighted percentage error. For heterogeneous data. |
| [WRMSE](lib/errors/wrmse/Wrmse.md) | Weighted RMSE | Weighted root mean squared error. Custom observation weighting. |