TRADING SYSTEMS
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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