Classic Laguerre Filter
The original Laguerre filter from John Ehlers' 2002 'Time Warp' paper.
Usage
Use when a smooth trend estimate with controllable lag using only 4 state variables is needed. Preferred over long EMAs when computational memory is constrained.
Background
The Classic Laguerre Filter uses four first-order IIR sections sharing the same gamma coefficient. In Cybernetic Analysis (2004) Ehlers shows gamma maps directly to an effective period, making it highly tunable with minimal computation.
Parameters
gamma(default: 0.8): Smoothing factor (0.0 to 1.0)
Formula
[ L_0 = (1 - \gamma) \cdot Price + \gamma \cdot L_{0,t-1} ] [ L_1 = -\gamma L_0 + L_{0,t-1} + \gamma L_{1,t-1} ] [ L_2 = -\gamma L_1 + L_{1,t-1} + \gamma L_{2,t-1} ] [ L_3 = -\gamma L_2 + L_{2,t-1} + \gamma L_{3,t-1} ] [ Filt = \frac{L_0 + 2L_1 + 2L_2 + L_3}{6} ]