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> I'm wondering, in the following expression:
> LRS = LinearRegSlope(xaverage(Price,20)-xaverage(Price,15), 10);
> shouldn't the longert term average be subtracted from the shorter term
> average instead? Ie,
> LRS = LinearRegSlope(xaverage(Price,15)-xaverage(Price,20), 10);
Good catch. Typo on my part.
For anyone wondering what I'm doing here:
xaverage (or any average) is a lowpass filter. It filters out
the high-frequency component of the signal and passes the lower
frequencies. That's why the xaverage is smoother. The noisy
jittery parts of the signal are the high-frequency components.
C-xaverage is a highpass filter. It subtracts xaverage's lowpass
frequencies from the raw price signal, leaving the high freqs.
That way you have all the noise, but you remove some of the trend
component. Not generally real useful, because noise just gets in
the way of trading decisions.
xaverage - xaverage is a bandpass filter. It filters out low
frequencies (trend) AND high frequencies (noise) leaving you only
the cyclic information.
I can never remember the exact xavg-len to frequency conversion
process, but we don't need to know the exact freqs here anyway.
Just notice that xaverage(Price,15) is a faster, noisier signal
than xaverage(Price,20); that means the len=15 xavg has a higher
cutoff frequency, allowing more high-freq noisy signal through.
So we want it to define the top frequency of our bandpass, so it
passes all frequencies below its cutoff. That means it's a
lowpass so it's the positive component of the bandpass
calculation. Conversely the len=20 xavg has a lower cutoff
frequency, so we want it to define the bottom of our bandpass.
It should pass frequencies above its cutoff, meaning it's a
highpass filter, so we use it in the negative component of the
bandpass calculation.
Clear as mud? :-)
Even if you don't understand the derivation behind it, you can
use this xaverage(Price,shortlen) - xaverage(Price,longlen) idea
to grab the cycle component of a price waveform, filtering out
the longer trend component and the shorter noise component.
Experiment with different lengths and different spacing between
the long/short lengths to see how it changes the results. For
example, using a larger value of longlen means your bottom cutoff
frequency is lower, so more low-frequency (trend) signal gets
through. Using a smaller value of shortlen means your top cutoff
frequency is higher, so more high-frequency (noise) signal gets
through. If you want less noise, increase shortlen. If you want
less trend, decrease longlen. But keep longlen > shortlen or
(like me) you'll invert your signal.
BTW I should have said the xavg-xavg signal was most similar to
Chris's summation(C-C[1]) signal. It still has some trend
component, just like his signal did. Running it through LRS just
detrends it further. And in fact LRS acts as a bandpass filter,
removing both noise AND trend. LRS actually does a better job of
filtering out the trend component than the highpass xaverage.
But I still think LRS(xavg-xavg) does the best job of extracting
the pure cycle component.
Gary
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