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lib/trends_FIR/ilrs/Ilrs.md
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# ILRS: Integral of Linear Regression Slope
# ILRS: Integral of Linear Regression Slope
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Trend (FIR MA) |
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 14) |
| **Outputs** | Single series (Ilrs) |
| **Output range** | Tracks input |
| **Warmup** | `period` bars |
### TL;DR
- ILRS computes the linear regression slope over a rolling window, then accumulates it via discrete integration (running sum) to reconstruct a smooth...
- Parameterized by `period` (default 14).
- Output range: Tracks input.
- Requires `period` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "John Ehlers took the slope of a regression line, integrated it, and got a smoother trend follower. Differentiate to find direction, integrate to find position. Calculus: still useful after 300 years."