Ultimate Bands
A Bollinger-style band using UltimateSmoother for the center line and standard deviation of the price-smooth difference for width.
Usage
Use as volatility bands that automatically widen during high-energy cycle phases and narrow during quiet phases. Better than fixed-multiple ATR bands in strongly cyclical markets.
Background
Ehlers Ultimate Bands compute upper and lower price envelopes using the RMS amplitude of the dominant cycle rather than a fixed ATR multiple. This makes the bands proportional to the current cycle energy, expanding when the market is actively cycling and contracting when it enters a low-energy consolidation.
Parameters
length(default: 20): Smoothing and SD periodnum_sds(default: 1.0): Standard Deviation multiplier
Formula
[ Smooth = UltimateSmoother(Close, Length) ] [ SD = \sqrt{\frac{1}{n}\sum_{i=0}^{n-1} (Close_{t-i} - Smooth_{t-i})^2} ] [ Upper = Smooth + NumSDs \times SD ] [ Lower = Smooth - NumSDs \times SD ]