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Arguing only in the most gentlemanly sense of the word of course :-)
I certainly agree with your motives to want to be able to backtest these
tools and share them completely. I just wish it was a bit easier!
Here's to the challenge though. Good luck!
Fred wrote:
>
> LOL ... I didn't think we were arguing ...
>
> In any case, while I would agree of course that the pupose of the
> development of any system or indicator is about improving one's
> trading and about making money in the markets, usually a step that
> plays a part in determining whether or not some tool is usable
> involves objective backtesting ...
>
> --- In amibroker@xxxxxxxxxxxxxxx <mailto:amibroker%40yahoogroups.com>,
> Andy Davidson <AndyDavidson@xxx>
> wrote:
> >
> > 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> <mailto:amibroker%
> 40yahoogroups.com>,
> > > Andy Davidson <AndyDavidson@>
> > > 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> <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> <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> <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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