Choppiness Index: another way of calculating fractal dimension.
Choppiness is a modern indicator based on ideas of chaos theory and fractal geometry. Benoit Mandelbrot was the one person most responsible for the great interest in the subject of fractal geometry. He showed how fractals can occur in many different places in both mathematics and elsewhere in nature. They could be found underlying cloud formations, waves, leaves, fingerprints, and sunflowers, and his ideas provided some exciting glue between mathematics and nature. Using computer graphics and with the help of IBM, Mandelbrot was able to show how to express fractal geometry using computer graphics.
While most of us think there are only whole number dimensions, like 1D, 2D, and 3D, in fractal geometry there exist fractional dimensions in between the whole number dimensions. So there are a number of fractal dimensions between a 1D line and a 2D plane. Fractals are basically a measurement of the dimensionality of a system; they are able to express different images based on the fractional nature of dimension.
E. W. Dreiss, a trader based in Australia, came up with the creative idea of using fractal geometry as a way to measure price movement in a security. He cleverly assigned a "dimension" to a price movement chart. A chart that was trending and linear could be given the whole dimension of 1 while a chart that was totally choppy and not trending could be said to have a dimension of 2. Somewhere in between these two values represented fractional states and different degrees of choppiness.
Compared to the Choppiness Index indicator, this version is using JMA for smoothing (to make it easier to spot the slope direction change of the choppiness index) and to make the values less volatile.
Choppiness Index: another way of calculating fractal dimension.Random Walk Index - JMA Smoothed
In order to avoid the too many signals that the regular Random Walk Index tends to produce, this version is using JMA for smoothing which significantly lessens the number of false signals.