Median Absolute Deviation Filtered SMA & BB

Median Absolute Deviation (MAD) is a robust measurement of variability and more resilient against outliers and small samples.

This experiment uses MAD as a means of filtering outliers from an SMA calculation. First we construct the equivalent of a Bollinger Band, but based on the median as the basis and a multiple(k) of MAD as the outlier cutoff.

k can be set a number of ways. As a simple multiple (3 - very conservative / 2.5 - moderately conservative / 2 - poorly conservative). Alternatively MAD can be used as an estimator of standard deviation by using a multiple of 1.4826 (SD1 - 1.4826 / SD2 - 2.9652 / SD3 - 4.4478).

Once we have a cutoff range an SMA is calculated with the outliers filtered out. Additionally a Bollinger band can be output using the filtered SMA as the basis and a multiple of the MAD instead of SD for the bands.