Fractal Adaptive Moving Average
An adaptive moving average that uses the fractal dimension of prices to dynamically change its smoothing constant.
Usage
Use as an adaptive moving average that slows dramatically during consolidation and speeds up during trending phases. Outperforms fixed-period MAs in ranging markets by avoiding false crossovers.
Background
The Fractal Adaptive Moving Average uses the fractal dimension of recent price action to adapt its smoothing constant. During trending markets the fractal dimension approaches 1 (a line) producing a fast-reacting EMA; during ranging markets the dimension approaches 2 (a plane) slowing the average dramatically to filter chop.
Parameters
length(default: 16): Length (must be an even number; odd values will be incremented by 1).
Formula
[ D = \frac{\log(N_1 + N_2) - \log(N_3)}{\log(2)} ] [ \alpha = \exp(-4.6 (D - 1)) ] [ \text{FRAMA}t = \alpha P_t + (1 - \alpha) \text{FRAMA} ]