V.7:3 (87-90): Moving averages and smoothing filters by John Ehlers

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 it—we 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 out.