Moving averages and smoothing filters
by John Ehlers
Moving averages are perhaps the single most widely used technical trading tool. While averages are
important tools, let's face itówe don't need computers to calculate them. Traders were using moving
averages long before simple calculators were commonly available. Traders simply computed the averages
by hand. Since we have the awesome power of sophisticated computers now at our fingertips, it's logical
to imagine that we can harness this power to create a better smoothing filter than the averages we now
use. I'll show that may not be so.
The object of a smoothing filter is to pass desired frequencies (like price cycles) and to reject the
undesired frequencies such as "noise" or "jitter" in everyday market action. An exponential moving
average (EMA) is a filter in this sense because it attenuates (that is, diminishes) the high frequency
variations while retaining the desired lower frequency variations.
Exploiting the computer's power, we can increase the complexity of a filter's transfer response to create a
"stonewall" filter that has a sharp cutoff response. Such a filter passes all signals below the cutoff
frequency almost without attenuation and rejects nearly all signals above the selected frequency. Thus,
low frequency waves, like cycles, are extracted from a series of prices while high frequency noise is cut