SYSTEM DESIGN
Simplifying Your Life
Moving Average Computations, Made Easier
by John F. Ehlers
Presenting programming tricks to simplify coding indicators and strategies.
A simple moving average of length N is computed
by adding N values and dividing the sum by N. The process is repeated on
a bar-by-bar basis. What could be easier? While conceptually simple, coding
for long moving averages can quickly become wearisome because there are
so many terms.
This tedium can be reduced by putting the summation in a loop, but looping
is difficult to achieve in some applications, such as Excel. Another simplifying
approach is to drop off the oldest value and add a new value to the moving
average. However, this requires computing the initial value of the long
moving average at least once. Here are two ways to compute the simple moving
average (SMA) with ease.
In Z-transform notation, a unit delay is represented by Z-1. The transfer
response is the output of the filter divided by its input. Thus, the transfer
response of an eight-bar simple moving average would be written as:
(Equation 1)
H(z) = (1 + Z-1 + Z-2 + Z-3 + Z-4 + Z-5 + Z-6 + Z-7)/8
...Continued in the December 2003 issue of Technical Analysis
of STOCKS & COMMODITIES
Excerpted from an article originally published in the December 2003
issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights
reserved. © Copyright 2003, Technical Analysis, Inc.
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