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Semantics aside, I think we're arguing the same point here. I also use a
correlation to the data to select the cycle parameters.
As I said the difference, in terms of output, between our methods is
that you get all the cycles in one go and I have to be a bit more
'manual' to get the full picture. The answers we get should end up being
approximately the same.
Your approach (providing it really does work!) is superior, no doubt
about it, because of that one difference. Obviously, being able to
back-test either method would be the ultimate goal. However, my
experience is that (a) I don't yet have the technical and/or
mathematical expertise to achieve that and, as you say, (b) any attempts
I have made so far have made the run-time very slow indeed. I'm working
on (a) but my feeling is that to get over (b) we are either going to
need a leap of ingenuity or a leap in computing power. It will be
interesting to see which comes first and when!
So having reached these conclusions myself a long time ago I decided to
either just keep it as an academic exercise and plod on with it when I
have the free time or to just go ahead and use what I've got,
backtesting validation or not. I'm personally glad that I did the
latter. From real trading results I now have faith in the method and
also in my application of it. Therefore, things should only be able to
get better if I can improve the indicator(s).
So when you say "it is about being able to objectively backtest" I have
to, respectively, disagree again. It is about inmproving one's trading
and about making money in the markets.
Unitl later then,
Andy
Fred wrote:
>
> No argument about Millard except that I would liken his doubly
> smoothed CMA to a regular CMA by making each of the components of
> Millards shorter ergo my 2/3, 1/3 comment so that they are measuring
> roughly the same thing ...
>
> If you don't like the word "dominant" then how bout ... "most
> prevelant" or the one that is arrived at as a result of it having the
> highest correlation to the data ... It's the last methodology I am
> using at the moment ... It's expensive in terms of run time but seems
> to be worth it.
>
> To me it is not necessarily about mechanical or nothing ... it is
> however about being able to objectively backtest ...
>
> With regards to divergence ... agreed ... many forms of this make for
> decent pattern recognition solutions ...
>
> Although there are Trigonometric ( as in Hurst's Appendix 6 )
> methodologies to extract all cycles at once ( like an FFT would )
> this is not the methodology I employed. They may all be done in the
> same AFL but in essence via multiple passes ... See my original
> English write up ...
>
> Regarding over/under engineering ... I agree ... It is hard to tell
> though without objective backtesting whether one has carried some
> approach far enough or too far or hopefully somewhere in between.
>
> --- In amibroker@xxxxxxxxxxxxxxx <mailto:amibroker%40yahoogroups.com>,
> Andy Davidson <AndyDavidson@xxx>
> wrote:
> >
> > A standard CMA has lag 17 bars for n=35
> >
> > Millard's Smoothed is an n-period MA smoothed by an n/2-period MA.
> So
> > the lag is (n-1)/2 + (n/2-1)/2
> > For n=35 this equals (35-1)/2 + (17-1)/2 = 17+8 = 25
> >
> > In his book Millard calculates an 11-week average of a 21-week
> average.
> > See his Table 7.2
> >
> > He also states further on that "a 15-week smoothed average would
> cause
> > the loss of 10 points at the end of the plot"
> > If n=15 then the lag is (15-1)/2 + (7-1)/2 = 10
> > A centred SMA of n=15 would have lag of just 7
> >
> > I don't agree with what you say in 1). Millard uses this CMA stuff
> in a
> > build up to his Cycle Highlighter (CH) indicator in Chapter 9. This
> > indicator does not attempt to extract the "dominant cycle" per se.
> When
> > I hear that phrase it reminds me of Ehler's language
> in "Cybernetic..."
> > but I won't divert onto that here.
> >
> > There are lots of cycles present in most price series, once you
> allow
> > for the noise and for long-term fundamental-driven trends and they
> can
> > all be "dominant" depending on what time-frame you are looking at
> and
> > what you are trading on. For example, I might be trading a 21-day
> cycle
> > and you might be more interested in a 52-WEEK cycle, depending on
> our
> > trading styles. So, *IF those cycles are present to trade on AND
> are
> > strong enough not to get lost in noise* then the CH indicator
> should be
> > able to pick EITHER of them out, depending on how you set the
> parameters.
> >
> > None of this is "touchy feely". *USED CORRECTLY* it works. I've
> traded
> > with it and I've had repeated success doing so. (Please, no calls
> for
> > trading records!) The success I have had though is through
> incorporating
> > it into my overall strategy. I do not rely on one indicator and I
> most
> > definitely do not automate. I agree that there needs to be some
> element
> > of automation in there, if for no other reason than for
> > scanning/exploring for suitable issues that show good cyclic
> behaviour.
> > To that end I have tried to automate the CH indicator as I
> discussed in
> > previous posts. So I think I answered your point 2) already. Let me
> know
> > if you need further clarification.
> >
> > However, I don't subscribe to the "Mechanical Or Nothing" school of
> > thought. Yes, the CH indicator works in a "general way"...and that
> is
> > good enough for me. It is not "very" general though. One of my
> other
> > analyses is based on divergence. Divergence works very well indeed,
> when
> > it works at all. And therein lies a problem. My own divergence
> indicator
> > probably has a 50-60% hit rate. I could make this work on its own
> with
> > decent money management rules, but when I combine it with an
> > *appreciation* of the cycles that hit rate number goes up quite
> > significantly. So you can see that I am using mechanical signals
> from
> > one method and then applying a discretionary filter based on my
> > appreciation of the cycle I wish to trade on. I do not need to
> be "no
> > hands"...I like my hands!
> >
> > A while back you sent a chart.png of the work you had been doing to
> > extract all the cycles from a waveform using Cleeton's methods.
> > Conceptually, there's no real difference between what you are
> trying to
> > do there and what the CH indicator does. The differences are that
> (a)
> > the CH indicator extracts cycles one-at-a-time whereas your tries
> to do
> > them all at once, and (b) there are no fancy mathematics (YET!) for
> > extrapolating to the right-hand edge. The extrapolation method I
> have is
> > quite crude...but please remember that cycles are quite crude too.
> The
> > amplitude and wavelengths are *never* constant. Over-engineering
> > something can sometimes be as dangerous as under-engineering.
> >
> > Regards,
> > Andy
> >
> > Fred wrote:
> > >
> > > Andy,
> > >
> > > In looking at your spreadsheet I understand what's there except
> > > for ...
> > >
> > > I'm not sure why a Millards smoothed should have more lag then a
> > > standard CMA ...
> > >
> > > Although I thought an even number would be required i.e. 34 or 38
> > > instead of 35 ...
> > >
> > > Millard would have calc'ed a 23 bar CMA and then a 11 bar of
> > > that ... or 25 and 13 if you prefer ... the lag would have been
> 11 + 5
> > > = 16, or 12 + 6 = 18 respectively ... where'd you get a lag of 25
> for
> > > 35 bars ?
> > >
> > > In any case what all these seem ? to be missing imho is ...
> > >
> > > 1. I don't think the dominant cycle is enough to do the job in
> > > terms of extrapolation and/or prediction by itself except in a
> very
> > > general way ...
> > > 2. What at least semi automated ( no touchy feely allowed )
> > > method are you gonna use to determine the CMA length to be used
> and
> > > then
> > > 3. How to process that info ...
> > >
> > > The AFL I have for Trig Fit, the output of which I posted on AB
> takes
> > > care of all 3 of the above with no hands ... run time is of
> course a
> > > different issue
> > >
> > > --- In amibroker@xxxxxxxxxxxxxxx
> <mailto:amibroker%40yahoogroups.com> <mailto:amibroker%
> 40yahoogroups.com>,
> > > Andy Davidson <AndyDavidson@>
> > > 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> <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> <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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Content-Description: "AVG certification"
No virus found in this incoming message.
Checked by AVG Free Edition.
Version: 7.1.409 / Virus Database: 268.13.27/517 - Release Date: 11/3/2006
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