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Miha Kralj
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lib/trends_FIR/ilrs/Ilrs.md
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| **Signature** | [ilrs_signature](ilrs_signature.md) |
- 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).
- **Similar:** [LSMA](../lsma/lsma.md), [LinReg](../../statistics/linreg/LinReg.md) | **Complementary:** R² for fit quality | **Trading note:** Integral of Linear Regression Slope; smoothed trend derived from cumulative regression.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
ILRS computes the linear regression slope over a rolling window, then accumulates it via discrete integration (running sum) to reconstruct a smoothed price-level signal. By differentiating (slope extraction) and reintegrating, ILRS acts as a low-pass filter that preserves trend direction while suppressing high-frequency noise more aggressively than LSMA. The integration step introduces a natural momentum quality: the output continues rising even as slope magnitude diminishes, making ILRS particularly effective for trend-following systems that need early exit signals based on slope deceleration.
@@ -140,4 +138,4 @@ O(1) per bar after warmup (the incremental sum pattern removes the N-scan). For
| Slope formula | Yes | `VFNMADD`, `VDIVPD` once prefix sums are built |
| Integral (prefix sum of slopes) | Partial | Sequential scan; parallel prefix available but overhead > benefit for N < 1000 |
Batch mode can precompute prefix sums vectorially then compute all slopes in parallel. The integral sum remains a sequential dependency. Net speedup for large series: ~2× over scalar.
Batch mode can precompute prefix sums vectorially then compute all slopes in parallel. The integral sum remains a sequential dependency. Net speedup for large series: ~2× over scalar.