QuanTAlib/lib/errors/rmse/Rmse.md

RMSE: Root Mean Squared Error

"MSE's more interpretable sibling that speaks the language of your data."

Root Mean Squared Error (RMSE) is the square root of MSE, providing an error metric in the same units as the original data while retaining sensitivity to large errors.

Mathematical Foundation

Formula

RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2} = \sqrt{MSE}

Properties

• Non-negative: RMSE ≥ 0
• Same units: Unlike MSE, RMSE is in original data units
• Outlier sensitive: Inherits MSE's penalty for large errors
• Always ≥ MAE: RMSE ≥ MAE due to Jensen's inequality

Usage

var rmse = new Rmse(period: 20);
var result = rmse.Update(actualValue, predictedValue);

// Batch calculation
var results = Rmse.Calculate(actualSeries, predictedSeries, period: 20);

Performance Profile

Metric	Score	Notes
Throughput	~15 ns/bar	O(1) with sqrt operation
Allocations	0	Pre-allocated ring buffer
Complexity	O(1)	Constant time per update

Related Indicators

• MSE - Mean Squared Error
• MAE - Mean Absolute Error