UltimateSmoother
An Ehlers filter with zero lag in the Pass Band, constructed by subtracting High Pass response from the input data.
Usage
Use when you need near-zero phase lag smoothing with very low ripple. It is Ehlers preferred smoother for applications where timing precision is critical.
Background
Ehlers designs the Ultimate Smoother in Cycle Analytics for Traders to minimize both lag and ripple simultaneously. It achieves near-zero phase shift across the passband while providing excellent attenuation of high-frequency noise, making it his preferred general-purpose smoother for cycle-sensitive applications.
Parameters
period(default: 20): Critical period (wavelength)
Formula
[ a_1 = \exp\left(-\frac{1.414\pi}{Period}\right) ] [ c_2 = 2a_1 \cos\left(\frac{1.414\pi}{Period}\right) ] [ c_3 = -a_1^2 ] [ c_1 = (1 + c_2 - c_3) / 4 ] [ US = (1 - c_1) Price + (2c_1 - c_2) Price_{t-1} - (c_1 + c_3) Price_{t-2} + c_2 US_{t-1} + c_3 US_{t-2} ]