Concept
Polynomial Regression
Polynomial Regression is a Statistics concept. The Library holds 7 implementations, each one a working definition you can pull into Quant.
Top Polynomial Regression indicators
7 total
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What is Polynomial Regression?
Polynomial regression fits a curved line to price by least squares: instead of a straight linear regression, the model adds squared, cubed, and higher powers of the bar index, then solves for the coefficients that minimize the squared distance between curve and price over a lookback window. Degree controls flexibility: degree 1 is a straight line, degree 2 a parabola with one bend, degree 3 allows two bends. Chart implementations usually draw the fitted curve through the window, often with bands offset by a multiple of the residual standard deviation, in the spirit of a standard-error channel.
The appeal is that real swings curve, and a straight fit misrepresents them; a low-degree polynomial can trace an arcing trend and expose acceleration or rollover in its right-edge slope. The costs are just as structural. Higher degrees chase noise and oscillate hardest near the window's edges, exactly where decisions are made; the entire curve is refit on every bar, so drawn history revises; and extrapolating a polynomial beyond its window is fragile, with small coefficient changes swinging the projected path widely.
How to calculate a polynomial regression
The fit is ordinary least squares with extra columns for the curvature terms.
- 1Choose a window N and a degree d. On charts, degree 2 or 3 covers most useful curvature; higher degrees mostly model noise.
- 2Build the predictors: the bar index and its powers up to d, usually centered or rescaled first for numerical stability.
- 3Solve the least-squares problem for the d+1 coefficients that minimize the sum of squared residuals between curve and price.
- 4Draw the fitted curve across the window, optionally adding bands at multiples of the residual standard deviation, and refit as each new bar arrives.
How traders use it
- As a curved trend baseline: the right-edge slope and its change give a read on trend direction and acceleration or inflection that a straight fit smooths away.
- As a mean-reversion frame: distance from the fitted curve, measured in residual standard deviations, flags stretched excursions, with band tags treated as fade candidates in ranging conditions rather than automatic signals.
- As a detrender: subtracting the fitted polynomial isolates the residual wiggle, a common preprocessing step before cycle or oscillator analysis.
- As a projection: some tools extend the curve forward as a scenario path. Treat it as a sketch of what happens if current curvature persists, not a forecast; reliability decays quickly outside the fitted window.
Polynomial Regression vs related concepts
Linear Regression: Linear regression is the degree-1 special case: one slope, no curvature. The polynomial's extra terms track arcing moves better inside the window, but they add overfitting and edge-instability risk the straight line does not have.
LOESS Smoothing: LOESS fits many small local regressions and stitches them together, so its shape is driven by neighborhoods of data. A polynomial regression fits one global curve, so a shock at one end of the window bends the fit everywhere.
Polynomial Regression Band: The band is the packaged application: the same fitted curve plus envelopes at a multiple of the residual deviation. The regression itself is the estimator; the band adds the volatility casing used for tag-and-fade or breakout reads.
More Polynomial Regression implementations
Related concepts · Regression & filtering
Concept family
Statistics
45 concepts mapped · 37 in the Library
Polynomial Regression FAQ
What degree should a polynomial regression use on charts?
Low. Degree 2 or 3 captures the curvature of most swings; each added degree buys flexibility at the cost of fitting noise and wilder behavior near the window edges. Degree is a bias-variance dial rather than a quality setting, so increase it only when residuals show clear systematic shape the current degree cannot express.
Does polynomial regression repaint?
As usually drawn, yes: the whole curve is refit each bar, so plotted history bends as new data arrives, and a touch that appeared on the curve earlier may vanish. The live right-edge value is what a system actually had at the time, so signal logic should be built on that, evaluated bar by bar (repaint-safe engineering).
Can a polynomial regression be projected into the future?
Mechanically it extrapolates, and some overlays draw the extension. Statistically it is the weakest use: outside the fitted window polynomial paths diverge quickly, and refitting one bar later can swing the projection substantially. Treat an extension as a visual scenario that assumes current curvature persists, and expect it to be revised.
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