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lib/statistics/polyfit/Polyfit.md

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 # POLYFIT: Polynomial Fitting
 
+| Property         | Value                            |
+| ---------------- | -------------------------------- |
+| **Category**     | Statistic                        |
+| **Inputs**       | Source (close)                          |
+| **Parameters**   | `period`, `degree` (default 2)                      |
+| **Outputs**      | Single series (Polyfit)                       |
+| **Output range** | Varies (see docs)                     |
+| **Warmup**       | `period` bars                          |
+
+### TL;DR
+
+- Polynomial Fitting computes a rolling polynomial regression of configurable degree over a lookback window, returning the fitted value at the curren...
+- Parameterized by `period`, `degree` (default 2).
+- Output range: Varies (see docs).
+- Requires `period` bars of warmup before first valid output (IsHot = true).
+- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
+
 Polynomial Fitting computes a rolling polynomial regression of configurable degree over a lookback window, returning the fitted value at the current bar. Degree 1 produces a linear regression endpoint (identical to LSQR), degree 2 produces a quadratic fit that captures curvature, and degree 3 produces a cubic fit that captures inflection points. The implementation solves the normal equations $\mathbf{X}^T\mathbf{X}\mathbf{a} = \mathbf{X}^T\mathbf{y}$ via Gauss-Jordan elimination with partial pivoting, evaluating the resulting polynomial at $x = 1$ (the current bar position). With $O(Nd + d^3)$ complexity per bar where $N$ is the period and $d$ is the degree, POLYFIT provides a general-purpose curve-fitting tool that subsumes linear regression and extends it to arbitrary polynomial order.
 
 ## Historical Context