TRADING SYSTEMS
Adapting To Market Conditions
Measuring Cycle Periods
by John F. Ehlers
Measuring cycle periods allows you to adjust your indicators
so they adapt to current market conditions. Here's how.
IF you want to make your indicators and
strategies adaptive to current market conditions, you must first measure
the cycle periods that are present in the data. Given that you know the
dominant cycle, you can then use that information to dynamically adjust
your computations. For example, you can set the observation period of the
relative strength index (RSI) to be half the dominant cycle. I have previously
described a practical way to use direct Fourier transform (DFT) to estimate
the market spectrum. But a DFT is not the only way to estimate the market
spectrum.
USING BANDPASS FILTERS
In this article I describe a way to use bandpass filters to make the
spectral estimate. Bandpass filters are advantageous in that the selectivity
and the filter transient response can be controlled. This is important
because not all filters are good for trading, since filters induce lag
in the output and therefore cause a delay in your making trading decisions.
In general, the more complicated a filter, the more lag is induced. The
simple two-pole bandpass filter is nice because it provides no lag at the
output for a steady state input signal at the frequency to which the bandpass
filter is tuned.
First, let's understand some basics about bandpass filters. The response
of the filter can be seen in Figure 1. This means that when equal amplitude
signals at all relative frequencies are applied to the input of the filter,
the filter rejects frequency components that are both higher and lower
than the filter's tuned frequency. The frequency components at the output
of the filter have their amplitudes shaped by the filter. The region within
relative frequencies -0.5 to +0.5 is the passband of the bandpass filter
because most of the energy getting through the filter falls in this range.
FIGURE 1: BANDPASS FILTER RESPONSE TO NORMALIZED FREQUENCIES.
Here you see the response of the filter. Note that most of the energy
getting through the filter falls within relative frequencies of the -0.5
to +0.5 range.
...Continued in the March issue of Technical Analysis of
STOCKS & COMMODITIES
Excerpted from an article originally published in the March 2008
issue of Technical Analysis of
STOCKS & COMMODITIES magazine. All rights reserved. © Copyright
2008, Technical Analysis, Inc.
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