Measuring Cycle Periods by John F. Ehlers
Measuring cycle periods allows you to adjust your
indicators so they adapt to current market conditions.
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, letís 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 filterís 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.