by John Ehlers
Averages have long been recognized as the best estimator of a random variable. Traders use moving
averages as trading signals or as components of trading systems, but the moving average characteristics
are seldom described for them. This is the first of a two-part article on moving averages to help promote
a wider understanding. I'll explore some interesting characteristics of several kinds of moving averages
and compare them in this article. In part 2, these characteristics will be applied to create a new kind of
leading indicator entry system. I modestly call this new system ELI for the Ehlers Leading Indicator.
A moving average is, quite simply, a filter. It provides a means for passing through certain information
we wish to see, while witholding (attenuating) data which would obscure or confuse our efforts to see a
particular pattern. Just as sunglasses filter out certain wavelengths of light so we can see a scene more
clearly, a moving average filters out certain data elements so the pattern we seek can be more readily seen.
The moving average is a type of low-pass frequency filter. The filter removes the high-frequency
variations to produce the familiar smoothed line or response, as engineers call it. Such filters are often
described in terms of their impulse response. An impulse is a sharp spike (of theoretically zero width)
that excites the filter (the moving average). Striking a bell is a simple example of an impulse response.
The bell's ringing slowly dies out with time and during this period several overtones may interact to form
beat notes. Because the ringing theoretically never completely dies out, this kind of filter is called an
Infinite Impulse Response (IIR) filter. All physically realizable filters are of this type.