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.

Two-Input Pattern

All error indicators in this category follow a consistent dual-input API:

// Streaming mode
var mae = new Mae(period: 14);
var result = mae.Update(actualValue, predictedValue);

// Batch mode
var maeSeries = Mae.Calculate(actualSeries, predictedSeries, period: 14);

// Span mode (zero-allocation)
Mae.Batch(actualSpan, predictedSpan, outputSpan, period: 14);

Indicator Status

Indicator	Full Name	Status	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.

Status Key: ✅ Implemented | 📋 Planned

Choosing an Error Metric

By Use Case

Use Case	Recommended Metrics
General accuracy	MAE, RMSE
Outlier-robust	MAE, Huber, MASE, MDAE, Tukey
Percentage interpretation	MAPE, SMAPE, MAPD, MAAPE
Bias detection	ME, MPE
Scale-free comparison	MASE, RAE, RSE, MRAE, TheilU
Model quality score	R², RSE
Log-scale data	MSLE, RMSLE
Gradient optimization	LogCosh, PseudoHuber
Quantile forecasting	Quantile Loss
Volume-weighted	WMAPE

By Properties

Metric	Scale	Outlier Sensitivity	Complexity
MAE	Original units	Low	O(1)
MSE	Squared units	High	O(1)
RMSE	Original units	High	O(1)
MAPE	Percentage	Medium	O(1)
SMAPE	0-200%	Medium	O(1)
Huber	Original units	Low (configurable)	O(1)
R²	0-1 (for good models)	High	O(1)
MDAE	Original units	Very Low	O(n log n)
MDAPE	Percentage	Very Low	O(n log n)
LogCosh	Original units	Low	O(1)
PseudoHuber	Original units	Low	O(1)
Tukey	Original units	Very Low	O(1)