Exponentially Smoothed Moving Averages
by Donald R. Lambert
If you were to do a survey of all the many trading systems that are in common usage, it is very likely
that two calculation methods would be found to be leading the pack by a great margin. They are simple
moving averages (SMA) and exponentially smoothed moving averages (ESMA).
Most texts involving ESMA's are sprinkled with phrases describing the choice of a particular smoothing
factor as being equivalent to a certain number of days' SMA, or weighted moving average (WMA).
Aside from differences due to there being two schools of thought on how to compute smoothing factors,
some people choose l/n and others choose 2/(n + 1), where n is the number of days that the smoothing
factor is supposed to equate to, but there is another very important consideration. That is, the impact of an
item of data disappears completely from an SMA or WMA of n days on the (n + l)st day but never leaves
an ESMA entirely.
I would propose, therefore, that a different technique be used to choose ESMA smoothing factors. Rather
than use just an SMA number of days (by whichever scheme) to choose the factor, we should instead use
two parameters. The first of these would be the percentage of original impact that we wish an item of
data to utilize in a time period, and the second to be the number of days in the time period that the
percentage should relate to.