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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
77 lines
3.1 KiB
Markdown
77 lines
3.1 KiB
Markdown
# RMSE: Root Mean Squared Error
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> *MSE's more interpretable sibling that speaks the language of your data.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Error Metric |
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| **Inputs** | Actual, Predicted (dual series) |
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| **Parameters** | `period` |
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| **Outputs** | Single series (RMSE) |
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| **Output range** | $\geq 0$ |
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| **Warmup** | `period` bars |
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| **PineScript** | [rmse.pine](rmse.pine) |
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- 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 sensitiv...
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- **Similar:** [MSE](../mse/Mse.md), [MAE](../mae/Mae.md) | **Trading note:** Root Mean Squared Error; same units as input, emphasizes large deviations. Most common accuracy metric.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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## Mathematical Foundation
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### Formula
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$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2} = \sqrt{MSE}$$
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## Properties
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* **Non-negative**: RMSE ≥ 0
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* **Same units**: Unlike MSE, RMSE is in original data units
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* **Outlier sensitive**: Inherits MSE's penalty for large errors
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* **Always ≥ MAE**: RMSE ≥ MAE due to Jensen's inequality
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## Usage
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```csharp
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var rmse = new Rmse(period: 20);
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var result = rmse.Update(actualValue, predictedValue);
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// Batch calculation
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var results = Rmse.Calculate(actualSeries, predictedSeries, period: 20);
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```
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## Performance Profile
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### Operation Count (Streaming Mode)
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O(1) per bar. Single-pass scalar transformation of (actual, forecast) pair; no lookback window required.
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| Error computation (subtract, abs/square/log) | 1-3 | ~3-8 cy | ~5-15 cy |
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| Running accumulator update (EMA or sum) | 1 | ~4 cy | ~4 cy |
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| **Total** | **2-4** | — | **~9-19 cycles** |
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Streaming update requires only the current actual/forecast pair and running state. ~10-15 cycles/bar typical.
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### Batch Mode (SIMD Analysis)
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| Operation | Vectorizable? | Notes |
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| :--- | :---: | :--- |
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| Element-wise error computation | Yes | Independent per bar; fully vectorizable with `Vector<double>` |
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| Reduction (sum/mean) | Yes | Parallel reduction; AVX2 gives 4x speedup |
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| Log/exp components | Partial | Transcendental ops; polynomial approx for SIMD |
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Batch SIMD: 4x-8x speedup for large windows. ~3-5 cy/bar amortized in vectorized batch mode.
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| Metric | Score | Notes |
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| :--- | :--- | :--- |
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| **Throughput** | ~15 ns/bar | O(1) with sqrt operation |
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| **Allocations** | 0 | Pre-allocated ring buffer |
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| **Complexity** | O(1) | Constant time per update |
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## Related Indicators
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* [MSE](../mse/Mse.md) - Mean Squared Error
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* [MAE](../mae/Mae.md) - Mean Absolute Error |