TRADING SYSTEMS
The MacGyver Of Indicators
Swiss Army Knife Indicator
by John F. Ehlers
You've probably never heard of this indicator, but it has
all the common functions such as smoothing and momentum generation. Find
out why it's going to be your new best friend.
This indicator does some unusual things,
such as band-stop and band reject filtering. Once you program this indicator
into your trading platform, you can perform virtually any technical analysis
technique with it. This unique general indicator results from general digital
signal processing (DSP) concepts for discrete signal networks that appear
in various forms in technical analysis.
Z-TRANSFORMS
The description of this indicator involves Z-transforms. Z-transforms
are a convenient way of solving difficult difference equations in much
the same way that LaPlace transforms are used to solve differential equations
in calculus. Difference equations arise from the use of sampled data, the
way we have in technical analysis: Daily bars sample price data once a
day. Intraday bars sample price data every minute, hour, or whatever. The
concept is the same regardless of the sampling rate. In Z-transforms, Z-1
stands for one sample period of delay. For simplicity, I will always refer
to daily bars as the sample rate.
The transfer function of a discrete linear system is the ratio of the
output of the system divided by the input. Since both the output and input
can be described in terms of polynomials in the Z domain, we can write
the transfer function of a very simple indicator as:
In this case, both the input and output involve only a constant term
and a term having one unit of delay. By cross-multiplying and factoring,
we can describe the output in terms of the input as:
This equation is easily converted to indicator programming languages.
For example, in EasyLanguage, N units of delay is noted as [N] after the
variable. Thus, the transfer function programs to:
...Continued in the January 2006 issue of Technical Analysis
of STOCKS & COMMODITIES
Excerpted from an article originally published in the January 2006
issue of Technical Analysis of STOCKS & COMMODITIES magazine. All rights
reserved. © Copyright 2005, Technical Analysis, Inc.
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