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You won't need the math texts to get though Hurst's course
material ... What you will need is time and patience ...
The 2 / 3 factor is in essence I thought what you were advocating
i.e. the first cycle length being twice the second ...and the lag
being the combo of 1 less then half of both ... Millard suggests such
a methodology in chapter 7.
The Hurst "Like" DE AFL I posted in the library was an interesting
project ... It seems however that the points could be better picked
then by using CMA's ... But that's another exercise ...
--- In amibroker@xxxxxxxxxxxxxxx, Andy Davidson <AndyDavidson@xxx>
wrote:
>
> Don't worry Fred, straight talk is good for us all :-)
>
> I'll think about that 2/3 factor tomorrow - it's late here and my
brain
> is aching.
>
> I ordered the Cleeton book a while back but it still hasn't
arrived. I
> think it'll make for a nice relaxing Xmas read! I've got the book
by
> Hurst (Profit Magic), but I froze when I got to Appendix 6 and so I
> think I need Cleeton as you suggest! The Hurst course is on the
list as
> well, but first I think I'll have to get some old Maths texts out
of the
> attic and get the grey matter working again in that respect. My
maths is
> sadly lacking also and I feel it's really not adequate to take me
any
> further than I've got without some hard graft. Oh well, needs must
I
> suppose.
>
> As far as channels go, I had a look at your Hurst DE quickly today.
I
> played with Hurst-like channel trading myself a while back (when I
was
> still a naive Metastock user - yeah, I know, but it was OK for at
least
> that). I found that my skills were below that needed to tackle the
> extrapolation problem and so it was simply a matter of using
discretion
> and 'eyeballing' a la Hurst.
>
> That was when I found Millard's book and latched on to his Cycle
> Highlighter. To me it was (and still is) a simple and effective way
of
> determining the cycles if you have a bias towards discretionary
trading
> as I currently do. And by nature it is a normalised plot, so it
seemed
> logical to me to go about extrapolating on that plane before I
tried to
> tackle the price plot. However, I am now convinced (thanks in no
small
> part to yourself) that it is worth pursuing further with the
ultimate
> aim of automating the whole cycle-extraction process.
>
> So here's to the next step of the journey...hard graft and all.
>
>
> Fred wrote:
> >
> > Thanks for the description ... It wasn't a sarcastic comment per
> > se ... It is imho a benefit to be able to hear from authors of
code
> > what the process is that is going on as opposed to someone
> > unfamiliar with the code having to dig it out ...
> >
> > I agree with your comments in 1 & 2 ... I had initially
implemented
> > Millard's CMA in the Hurst DE I posted in the library this way ...
> >
> > Lag = int(Period / 2);
> > CMA = Ref(MA(MA(Data, Lag), Lag), Lag);
> >
> > It would seem though after reading Millard more carefully that a
> > better implementation is something like
> >
> > CMAL1 = Int(Period * 2 / 3);
> > if (CMAL1 < 5)
> > CMAL1 = 5;
> > If (CMAL1 % 2 == 0)
> > CMAL1 = CMAL1 + 1;
> > CMAL2 = Period - CMAL1;
> > If (CMAL2 % 2 == 0)
> > CMAL2 = CMAL2 + 1;
> > Lag = (CMAL1 - 1) / 2 + (CMAL2 - 1) / 2;
> >
> > CMA = Ref(MA(MA(Data, CMAL1), CMAL2), Lag)
> >
> > The only potential problem I see with this approach is it makes
the
> > minimum overall CMA Length 8.
> >
> > For the current AFL I implemented a simple CMA ... no muss /
> > fuss ... The reason is that the CMA would be sampled and
potentially
> > smoothed again ...
> >
> > I don't know whether or not you have Hurst's PM but he covers (
very
> > quickly ) the topic of pulling out the coeff's for multiple cycles
> > simultaneously in what is to me any way some rather complex math
in
> > Appendix 6 ... But then I'm hardly a math Wiz ... If you are
> > interested in this kind of thing I would strongly recommend
> > Cleeton's book which while out of print is still readily available
> > at Amazon and other places for a few bucks used. He discusses how
> > to perform a similar operation for one cycle and for multiple
cycles
> > simultaneously with one of the early steps being sampling of the
> > CMA ... He uses those points directly and as you can tell from my
> > description I opted for this approach more or less as well which
> > seems to produce some interesting results without requiring
Gaussian
> > Elimiation to solve multiple simultaneous equations.
> >
> > --- In amibroker@xxxxxxxxxxxxxxx <mailto:amibroker%
40yahoogroups.com>,
> > Andy Davidson <AndyDavidson@>
> > wrote:
> > >
> > > Hi Fred,
> > >
> > > It's good to be able to get back on this subject again,
especially
> > as it
> > > looks like there's a few of us who are 'into' cycles.
> > >
> > > Your work-in progress looks very interesting I must say. I
> > particularly
> > > like the idea in step 5 to reduce the data before finding a
> > > fit...brilliant in its simplicity. I also think your equation in
> > step 6
> > > will help me out...but without getting into that, here's the
> > general
> > > logic of my approach for comparison (and I take the sarcastic(?)
> > comment
> > > about explaining in English...I didn't do a good job of notating
> > the
> > > script properly!)
> > >
> > > 1. Calculate *two* CMAs using triangular-smoothed MAs. CMA1 is
n-
> > periods
> > > length and CMA2 is n/2-periods. Both periods are rounded up to
the
> > > nearest odd number.
> > > 2. CMA1 allows wavelengths > n-periods to pass and filters out <
> > > n-period waves. CMA2 allows through all cycle wavelengths > n/2-
> > periods
> > > and filters out those < n/2. Therefore, subtracting CMA2 from
CMA1
> > will
> > > give us the cycle (or combination of cycles if we're unlucky
> > enough, or
> > > have our value of n wrong) that lies between n/2 and n.
> > >
> > > Steps 1 and 2 are as per Millard's "Cycle Highlighter" (CH),
> > except he
> > > states that the best results are obtained with CMA1 being an SMA
> > and
> > > CMA2 being a Weighted MA. He also says CMA1 periods should be
> > *equal* to
> > > the wavelength to be isolated. This does work but, through
> > > experimenting, I have found that Triangular-MAs are best for
both
> > as
> > > they offer the superior smoothing-to-lag trade off. Furthermore,
> > the
> > > periodicity of CMA1 should be x1.5 the cycle you want (making
CMA2
> > > therefore x0.75). The logic still holds up and the results are
> > better
> > > IMO, with a more sine-like output.
> > >
> > > 3. Based on user-inputs (see below) I then generate an
artificial
> > sine
> > > wave. This is *anchored to the CH at its most recent (i.e.
> > confirmed)
> > > peak or trough*.
> > > 4. Correlation coefficients are calculated between (a) the sine
> > wave and
> > > the CH (or price - depending on user input) over the 'lookback'
> > period
> > > (see below) and (b) the sine wave and the price in the 'end
zone'
> > (i.e.
> > > the no-data zone for the CH at the right-hand edge).
> > >
> > > Inputs:
> > > "SINE WAVELENGTH" - this determines if the wavelength of the
sine
> > is (a)
> > > "as per the base cycle (CH)" (i.e. there is no attempt to 'fit'
> > the two
> > > curves beyond the anchor point) or (b) a "best fit". In the
second
> > case,
> > > the sine wavelength will depend on:
> > > "BEST FIT # RECENT CYCLES" - this is the number of full,
completed
> > > cycles of the CH where the correlation is measured. The start
> > point of
> > > X-cycles back is shown by a blue and red tick on the indicator.
If
> > > option (b) is chosen above the average wavelength of the CH is
> > measured
> > > in the zone from the blue tick to the end of its plot. This
value
> > is
> > > assigned to the sine plot. If option (a) above then we just get
X-
> > cycles
> > > back of both plots at the same periodicity.
> > >
> > > All the above is as per the first indicator I posted. The
> > following
> > > loops are done in the auto-fit version:
> > >
> > > 5. A loop from "Wavelength Min" to "Wavelength Max" is performed
> > to find
> > > the highest total correlation coefficient (a weighted average of
> > the
> > > 'CH/sine' and the 'sine/end-zone price' values).
> > > 6. The series of loops is repeated for "#Cycles Min" lookback up
> > to 5
> > > cycles lookback. I chose 5 as an arbitrary number...it's slow
> > enough as
> > > is and very rarely do you get a decent correlation going that
far
> > back.
> > > Obviously though when you do, you take notice.
> > >
> > > That's as much as I can tell you right now about the logic. Does
> > it
> > > work? Well, with the usual caveats blah-blah-blah, I would say
> > that it
> > > has been a very useful tool for me for a while now *in
conjunction
> > with
> > > other confirming and entry methods*
> > >
> > > Bear in mind that the purpose of the indicator is to find the
> > *clearest*
> > > cycle amongst those present, i.e. the one that conforms most
> > closely to
> > > a sine wave, and is therefore tradeable *on that time frame*. I
> > will
> > > manually switch between time-frames to get the various major
> > cycles
> > > (e.g. 1-hour, 4-hour, daily and weekly charts). Work on 'auto-
ing'
> > all
> > > that would be very processor intensive and requires further
> > thinking.
> > >
> > > The plot you sent seems to bear out a further truth about
trading
> > with
> > > cycles, one that I've experienced with this indicator more than
> > once:
> > > i.e. short-term cycles (measured in hours and a few days) are
less
> > > tradeable than longer-term ones (measured in a few days upwards
to
> > weeks
> > > & months). Certainly, in the plot you sent, most of the smoothed
> > price
> > > behaviour can be explained by the interaction of the two longest
> > > measured cycles (dark blue and cyan).
> > >
> > > Anyway, I look forward to ploughing through all the good stuff
> > you've
> > > already posted and hope you can help keep this thread going.
> > There's
> > > lots of really cool stuff going on here.
> > >
> > > Cheers for now,
> > > Andy
> > >
> > >
> > > Fred Tonetti wrote:
> > > >
> > > > Andy,
> > > >
> > > >
> > > >
> > > > Can you describe in English what your AFL does ? ...
> > > >
> > > >
> > > >
> > > > I've been playing with a Trig Fit a la Claud Cleeton the steps
> > for
> > > > which I would describe as follows ...
> > > >
> > > >
> > > >
> > > > 1. Optional - Normalize the input i.e. Data = log10((H + L) /
2)
> > > >
> > > > 2. Calc an arbitrary length ( Parameterized but 11 at the
> > moment )
> > > > centered moving average ( CMA ) of the data
> > > >
> > > > 3. Calc a 1st order least squares fit ( LSF ) of the CMA over
> > the
> > > > period desired ( from / to range marker )
> > > >
> > > > 4. Subtract the LSF points from the data points resulting in
> > detrended
> > > > data.
> > > >
> > > > 5. Take an n-bar sampling of the detrended data. This array
> > with
> > > > "holes" or "gaps" in it needs either to be compressed or have
> > the
> > > > "gaps" filled ... I elected ( for the moment ) to calc a cubic
> > spline
> > > > to fill the gaps ( interpolation ) ...
> > > >
> > > > 6. Calc a LSF of the detrended data resulting in the coeffs
for
> > the
> > > > Trig equation Y = A Cos wX + B * Sin wX
> > > >
> > > > 7. Calc the correlation of the resulting sin wave to the
> > original
> > > > detrended data.
> > > >
> > > >
> > > >
> > > > Repeat steps 5 & 6 varying n from 1 to ? looking for n where
the
> > > > correlation is the highest. This should yield the equation or
> > data
> > > > points that most closely correlate to the detrended data.
> > > >
> > > >
> > > >
> > > > 8. Subtract the points in the sin wave from the detrended data
> > > > resulting in a modified detrended data.
> > > >
> > > >
> > > >
> > > > Repeat steps 5 - 8 looking for the next most significant
cycle.
> > This
> > > > can be done repeatedly until overall correlation stops getting
> > better
> > > > and usually results in 2 - 6 cycles ...
> > > >
> > > >
> > > >
> > > > See attached ...
> > > >
> > > >
> > > >
> > > > The white line in the upper graph is detrended price ...
> > > >
> > > > The alternating green / red line is the trig fit, in sample up
> > to the
> > > > vertical line and out of sample projection afterwards ...
> > > >
> > > > The lines in the bottom section are the individual cycles
found
> > in the
> > > > data.
> > > >
> > > >
> > > >
> > > > Sometimes the projections are almost clairvoyant ... run time
> > however
> > > > is anything but quick ...
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
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>
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