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Here's a little explanation.
The reason the band values change for future dat in the code that I
presented is that the widths are calculated based on 2 standard
deviations from the mean.
I believe this to be valid because the act of centering the MA makes
the distribution about the centered moving average a true average of
the data valid to the bar period/2. Therefore, since the
mathematical operation is an average, and if we assume some cycle is
currently active in the form of a sinusoid, then the distribution
should be close to a normal distribution if enough data points are
taken, so standard deviation is the proper way to describe the
envelope width if its a normal distribution.
In fact statisticians call standard deviation with the greek letter
sigma - ala sigma bands - so that's probably why Maggio calls his
bands 'sigma bands'.
Here's the calculation for the bandwidth in terms of percent:
dp1=LastValue(Ref(StDev( (Close-cma1)/cma1, k*p1 ),(p1+1)/2-1));
where k=3 means that the standard dev is calculated over 3x the
period number of data points.
Using Lastvalue() makes the width a constant for all time based on
today's calculation. Therefore as data is added the bandwdiths
change and the way I have it coded it changes for all time. Its
almost a derivative of Bollinger bands. Bollinger was on the right
track he's just using the average incorrectly and standard deviation
does not describe the price distribution about a non-centered SMA
which is why his bands vary in width with the volatility of the
stock price movements.
I will bet you almost anything Maggio's charts do roughly the same
thing with whatever smoother or centerline calculation filter he's
using. There are many ways to calculate the centerline. His chart
could simply be a smoothed and centered SMA. You could easily smooth
a CMA with a parabolic curve fit or with various forms of
regression. However, he still needs to project the bands forward in
time using some method.
If you are really amibitious you should investigate least squares
regression fitting of trigonometric functions. I can create
beautiful DE bands with them using a different program that I wrote.
You still need to project forward in time, however, so that's really
the rub. There are likely much better ways of projecting the line
forward than I presented here using various regression techniques.
Learning something about digital signal processing is probably also
key.
In evaluating Maggio's service ask yourself a few questions. Why
create a for pay website to sell the idea to others if it works so
well? Why not just trade your way to financial freedom and retire?
Beware of snake oil. Maybe he's got something good there - I have to
admit it looks good - but I sure don't blindly trust a web site.
I'm sure a discretionary trading system could be built using
envelopes and oscillators that would perform fairly well, however
there would really be no way to backtest it. Forward testing or
trading would be the only way to do it.
-ace
--- In amibroker@xxxxxxxxxxxxxxx, "Fred" <ftonetti@xxxx> wrote:
> Dimitris / WaveMechanic,
>
> If the length of the CMA is n then
>
> The CMA can only be calculated up to n/2 bars ago after which it
must
> be extrapolated via some technique.
>
> So for example if one wanted to plot a 250 bar CMA showing the
> history of where it had been at time of original calculation then
one
> would need to,
>
> - At bar 375 calculate the CMA for bars 1 through 250 and
extrapolate
> for bars 251 through 375. This would provide the initial 250
> plottable points.
>
> - At bar 376 calculate the CMA for bars 2 through 251 and
extrapolate
> for bars 252 through 376. this should add one and only one
additional
> plottable point i.e. the one at bar 376.
>
> - This process could then continue up through the current bar.
>
> Someone made mention of Jan Arps Sigma Bands code for TradeStation
> which although available for usage in TS is not viewable. It does
> however provide the capabilty of showing both the historical past
> datapoints as originally calculated as well as the current
picture.
> The only similarity between these would be the CMA for the cureent
> and any future bar.
>
> See his description here ... http://www.janarps.com/SigmaBands.htm
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "wavemechanic" <wd78@xxxx> wrote:
> >
> > ----- Original Message -----
> > From: DIMITRIS TSOKAKIS
> > To: amibroker@xxxxxxxxxxxxxxx
> > Sent: Saturday, February 21, 2004 3:18 AM
> > Subject: [amibroker] Re: Sigma Bands
> >
> >
> > Wayne,
> > Sorry, I can not agree that the history of the signals is
> meaningless.
> > I need always to check any trading idea from its past behavior.
> >
> > Spoken like a true system trader. However, looking at
Maggio's
> description of the bands it is not clear to me that there should
be
> any change as new data is added, reflecting the fact that the
bands
> are simply the sigma of the % change of the data from the CMA.
This
> is a bar by bar calculation that does not change as new data is
> added. Perhaps, as you suggest, the problem lies in the way CMA
is
> calculated by the code. If so there must be a way around this
> problem, as evidenced by the fact that a manual calculation of CMA
> does not look into the future but simply centers a MA within the
> incremental period of another MA. So one needs to make code
> duplicate the manual calculation which is straightforward. Does
not
> sound like rocket science. And extrapolation of the CMA does not
> change its previously established values. However, even when
things
> are working right neither Sigma Bands or Hurst Channels by
themselves
> provide a mechanical buy/sell signal. No problem for
discretionary
> traders but system traders will need some "antacid" in order to
avoid
> heartburn. LOL.
> >
> > Dimitris Tsokakis
> > > Dimitris,
> > >
> > > I think you don't get that 'signals of the past' are in the
> past.
> > It's
> > > history and as such is meaningless. Hurst developed his work
> before
> > > computers had the power to do billions of computations per
> second.
> > > Therefore, the idea of backtesting his work is a waste of
time.
> > >
> > > The Sigma Bands we are discussing seem to be a derivative of
> the
> > Hurst
> > > Dependency Envelopes, so ably programmed by Ace... and much
> > appreciated
> > > too. I feel there is nothing at all to be gained from 1)
> looking
> > into
> > > the past or 2) trying to guess the future. I want to know
what
> is
> > > happening right now. The Sigma Bands MAY offer some insight
> into
> > what
> > > the market is saying now, but should never be used to trade
any
> > market
> > > by themselves. This information should always be used as
> > confirmation of
> > > other indicators and trading techniques.
> > >
> > > Computers will never replace the human brain.
> > >
> > > Wayne
> >
> >
> >
> > Send BUG REPORTS to bugs@xxxx
> > Send SUGGESTIONS to suggest@xxxx
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