[Haskell-beginners] Simple Moving Average of a list of real numbers

[John Souvestre]

 > Oh, sorry. Statistics is down the hall =)

There is another often used method which might be worth considering.  If you
don't need the absolute accuracy that the "boxcar" moving average gives, then
perhaps a exponentially weighted moving average (aka: exponential filter) will
do.  It has the advantage of being easier to code, requiring less CPU power
(normally), and needing only one variable for long term storage.

There a good description at:

    http://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average

Simply put, you save only the result, not the individual sample.  To update it
with a new sample you first remove the "equivalent" of one sample then add
your new sample.  How do you remove the oldest sample?  You can't, since you
didn't save it.  Instead you remove 1/n'th (for averaging over n samples) of
the previous result, then add the new sample.

If you think about it, the longer a sample has been part of the result, the
less effect it has on the result - exponentially less.  This is why I said it
isn't as accurate as the boxcar method.  But for many situations (most of the
ones I've run into) it suffices and indeed can be better since it dampens
(filters) step changes.

As an equation:

   average_new = average_old - (average_old / n) + (sample_new / n)

Or tweaking for efficiency:

    average_new = average_old + ( (sample_new - average_old) / n )

Note:  You need to use floating point numbers for the calculation and
resulting average, even if the samples are integers.  Also, choosing a binary
number for n should help speed up the division, if the math pack takes
advantage of it.

I realize that this doesn't directly address the question which Alex posed,
but I thought that perhaps it might be of interest as an alternative.

John

    John Souvestre - New Orleans LA - (504) 454-0899

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