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I hear what you say...my argument probably sounded fairly circular in
that respect. However, as I said, the purpose of the whole exercise for
me was to see in practice what all the theory was telling me. I didn't
miss the point - I just wanted to prove to myself, visually, that b) and
d) were essentially the same. In the process I also managed to show that
I was wrong to be using the Triangular MA *for this purpose* and that b)
(or d)!!) would be better suited as they have less lag for a similar, if
not better, result.
Fred wrote:
>
> With regards to d) ... I think you still missed my point about CMA's
> as I think what I did with the Hurst "LIKE" DE was to use what was
> straight out of chapter 7 of Millard ...
>
> n = Overall CMA length
> n1 = The first CMA Length = n * 2 / 3
> n2 = The second CMA Length = n * 1 / 3
>
> As a result:
>
> n1 = 2 * n2
>
> This is just like what you describe in b) ...
>
> The Trig ( or Cos and/or Sin ) fit of data is a different animal ...
> Because I knew I would be doing "sampling" of the CMA, I found the
> CMA part of this to be relatively unimportant ... I don't mean to
> imply that using one is a waste of time, it isn't but the exact
> configuration and length of it appears to be somewhat unimportant as
> it seems just having some form of smoothed data that doesn't lag is
> sufficent to drive the rest of the process. When Cleeton's book
> catches up with you, you'll know where I'm coming from.
>
> --- In amibroker@xxxxxxxxxxxxxxx <mailto:amibroker%40yahoogroups.com>,
> Andy Davidson <AndyDavidson@xxx>
> wrote:
> >
> > Fred,
> >
> > Long post I'm afraid, but bear with me...
> >
> > Since our last conversation I've been doing some head-scratching on
> > which method of CMA is best for extracting cycles. After re-reading
> > Millard and then trying to theorise my way in ever-decreasing
> circles
> > about what *should* be the best way, I decided to try to experiment
> and
> > find out what works best *in practice*. I've attached the results
> in the
> > form of plots and a summary spreadsheet for your (or anyone else's)
> > interest. Here's the logic behind the method (AFL code posted below
> for
> > sake of completeness) :
> >
> > 1. I created two independant sine waves and a 'noise' component.
> These
> > individual components are plotted in the top pane.
> > 2. I then added these together to create a composite 'price-like'
> plot -
> > plotted in grey in the bottom pane.
> > 3. Four different kinds of Centred-MA (see below) were then plotted
> on
> > the bottom pane, with the composite as an input. The aim was to
> select a
> > periodicity for each CMA that would filter out the noise and the
> shorter
> > wavelength cycle (cycle 2), leaving the closest possible
> representation
> > of the longer cycle 1.
> > 4. The lag, wavelength and amplitude of this CMA plot were then
> > *measured* (i.e. they weren't deduced theoretically, but were
> actual
> > observed values).
> > 5. The values were compared on the spreadsheet.
> >
> > The four different CMAs were based on:
> > (a) Simple MA. The most basic centred SMA
> > (b) Millard's "Smoothed Average" from Chapter 7...i.e. an MA of
> > n-periods which has been smoothed again by an MA of n/2 periods.
> > (c) Triangular MA. This is an n/2 MA of an n/2 MA
> > (d) Custom MA. This is per your last email with the first MA being
> > n*0.75 and the second being half that.
> >
> > The Triangular MA has the same lag characteristics as a Simple MA.
> > However, in order to get the same *filtering* effect (i,e, to take
> out
> > cycle 2 completely) you have to near-enough double the periodity,
> which
> > then obviously takes the lag up. Experimenting seems to suggest
> that you
> > don't actually have to double it, which I guess is why I settled on
> a
> > multiplying factor of 1.5 for my Cycle Highlighter indicator. I
> think I
> > originally settled on 1.5 after mis-reading Millard's section on
> the
> > "Weighted MA" and have therefore been using something which was
> > nearly-correct but for the wrong reasons! Oh well, at least I have
> a
> > better idea now. However, the results of this seem to suggest that
> 1.75
> > would be a better number, so I've changed my indicator accordingly.
> I'm
> > sure there's good theory behind why this should be so, but I can't
> think
> > it through. Can you?
> >
> > So anyway, all that testing seems to show is that Millard's
> Smoothed
> > Average is the best for this purpose. My triangular MA seems to
> have
> > been suffering too much lag than necessary, for an output which
> also
> > suffers more damping. There seems to be nothing to choose between
> your
> > "Custom" CMA and the "Smoothed Average". This is obviously because
> they
> > are basically the same thing. Both are MAs smoothed by another MA
> half
> > the first's length. The fact that the "Smoothed Average" starts off
> with
> > and n-period MA and the "Custom" one starts with n-periods*0.75,
> just
> > means that the latter has to have "n" ramped up to provide the same
> > filtering/smoothing effect.
> >
> > OK, so far so good. I've decided to ditch the Tri-CMA in favour of
> the
> > "Smoothed CMA". But here's another question. Millard states
> ("Weighted
> > Average" section) that for those of us with computers(!!) it is
> > preferable to chose a centrally-weighted MA. Anyone know how to do
> that
> > without slowing things down even more? Is that the same as the
> geometric
> > mean?? My maths really is too rusty. The standard WMA function is
> no
> > good as it applies the maximum weighting to the *most recent* bar.
> We
> > would need, for example, in a 7-bar MA to have a weighting sequence
> of
> > 1-2-3-4-3-2-1
> >
> > That'll do for now. Tomorrow's job is to add a third, longer, cycle
> and
> > see how extracting the middle cycle goes.
> >
> > Cheers,
> > Andy
> >
> >
> > Fred wrote:
> > >
> > > 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
> <mailto:amibroker%40yahoogroups.com> <mailto:amibroker%
> 40yahoogroups.com>,
> > > Andy Davidson <AndyDavidson@>
> > > 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>
> > > <mailto:amibroker%40yahoogroups.com> <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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