Now With Less Lag
Zero-Lag Data Smoothers
by John F. Ehlers
Here's a technique that can reduce lag to nearly zero.
A causal filter can never predict the future. As a matter of fact, the laws of nature demand that all filters must have lag. However, if we assume steady-state conditions - that is, no new, disturbing events - there are techniques we can use to reduce the lag of these filters to nearly zero. It turns out that such filters are useful for technical analysts with which to smooth data, and perhaps create some fast-acting indicators. This is possible because the steady-state assumptions are almost, but not quite, satisfied in the short run. These techniques are not applicable to longer moving averages, because steady-state conditions do not continue over a long time span. There are superior techniques for creating longer-term averages, such as nonlinear filters or by removing undesirable cycling components from a composite price waveform.
Engineers would describe the zero-lag process as the placement of a zero in the filter transfer response such that the rate change of phase at zero frequency is zero. Traders, on the other hand, would understand the zero-lag effect as a relationship between the lag of a moving average and momentum.
In Figure 1, the solid line represents a steady-state price movement, and the dashed line represents a moving average of the price lagging by N bars. The lag is the horizontal span. An N-bar momentum has the vertical span as shown. By adding the N-bar momentum to the moving average, you can recreate the original price movement. In this way, you can create a zero-lag moving average.
Figure 1: STEADY STATE LAG COMPENSATION. Here you see the relationship between price and moving average.
...Continued in the July 2002 issue of Technical Analysis of STOCKS & COMMODITIES
Excerpted from an article originally published in the July 2002 issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights reserved. © Copyright 2002, Technical Analysis, Inc.
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