Laguerre Filter
A trend-following filter that excels at smoothing long-wavelength components using Laguerre polynomials and an UltimateSmoother base.
Usage
Use as a low-lag smoothing filter with only 4 elements of state. Ideal when memory-efficiency matters or when a highly responsive smoother for real-time streaming is needed.
Background
Ehlers introduces Laguerre filters in Cybernetic Analysis (2004), noting they achieve the response of much longer conventional filters using only four coefficients. The single gamma parameter controls the trade-off between lag and smoothness.
Parameters
length(default: 40): UltimateSmoother periodgamma(default: 0.8): Smoothing factor (0.0 to 1.0)
Formula
[ L_0 = UltimateSmoother(Close, Length) ] [ L_1 = -\gamma L_{0,t-1} + L_{0,t-1} + \gamma L_{1,t-1} ] [ ... ] [ Laguerre = (L_0 + 4L_1 + 6L_2 + 4L_3 + L_5) / 16 ]