Using Orthogonal Polynomials for Smoothing and Trading Signals
Summary
The article presents orthogonal polynomials as a way to smooth financial price series and extract components associated with averages, trends, and nonlinear shapes. It outlines Legendre, Chebyshev, Laguerre, and Hermite families, describes mapping prices into each polynomial’s domain, and explains that weighted polynomial components can be combined into a filter. The degree and lookback period affect the resulting behavior; higher degrees may amplify noise, and the period must exceed the polynomial degree.
Proposed applications include replacing a simple moving average in price-crossing rules, comparing two polynomial series, adapting CCI-like calculations, and supplying polynomial weights as machine-learning features. The article characterizes the approach as noise resistant and adaptable, but offers no concrete performance statistics or controlled comparison in the supplied text. It also notes that values update as new prices arrive, so the indicator can redraw; the examples should therefore be treated as exploratory signal construction rather than established predictive evidence.
Key ideas
- Orthogonal polynomial weights can form a smoothing filter whose shape depends on polynomial family, degree, and period.
- A zero-degree polynomial corresponds to a simple moving average, while higher degrees add trend and curved components.
- The article proposes price-crossing and two-polynomial rules as trading strategies based on the filter.
- Polynomial components can also be substituted into CCI-like indicators or used as machine-learning features.
- Higher degrees can add noise, and the described indicator changes as new prices arrive.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.