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lib/statistics/polyfit/Polyfit.md
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| **PineScript** | [polyfit.pine](polyfit.pine) |
- 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).
- **Similar:** [LinReg](../linreg/LinReg.md), [TSF](../../trends_FIR/tsf/Tsf.md) | **Trading note:** Polynomial curve fitting; captures non-linear trends. Higher order = more responsive but risk of overfitting.
- 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.
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- Gauss, C.F. "Theoria Motus Corporum Coelestium." 1809.
- Golub, G. & Van Loan, C. "Matrix Computations." 4th edition, Johns Hopkins University Press, 2013.
- Press, W.H. et al. "Numerical Recipes: The Art of Scientific Computing." 3rd edition, Cambridge University Press, 2007. Chapter 15 (Modeling of Data).
- Draper, N. & Smith, H. "Applied Regression Analysis." 3rd edition, Wiley, 1998.
- Draper, N. & Smith, H. "Applied Regression Analysis." 3rd edition, Wiley, 1998.