Some Preliminary Thoughts on the Moving Median

日期:2013/11/25

Some preliminary thoughts on the running median 2, 3, 4, 1, 7, 8, 9, 3.

A moving median of the first 5 is 3, of the next 5 is 4, of the next 5 is 7, of the next 5 is 8– it's a good indicator of trend. First recommended to me 53 years ago by Fred Mosteller, Chairman of Harvard's first statistics dept.

It is more stable than the moving average as outliers are removed from sample. It is easy to compute fast with computers for small running numbers like 5 or 100 by repeated sorts. For higher numbers, you can form two groups, those below the median and those above. As a new number comes up you place it in one of the two groups if higher or lower and take away the oldest number. Then adjust to make the two groups equal again. It is not used as much as the moving average so it shouldn't be hurt by front running or spikes when cross over occur. It has a defined distribution when the underlying distribution has inordinate extreme values as frequently occurs with Cauchy or similar distributions with infinite variance.



It's probably a good thing to use when using nearest neighbors as predictors, i.e using the median and running median to compute your predictors. It deserves testing in real life markets for real life applications.