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Hi,
The Central Limit Theorem states:
If a large number of random samples (of size 30 or more) are
collected, the means from a sampling distribution of means where
a) the mean of the sample will be equal to the mean of the population
b) The StDev of the sampling distribution is the standard error of
the mean and
c) when n is large (> 30) the sampling distribution of means is
approximately normally distributed regardless of the shape of the
distribution of the population as long as the sample size of each
sample is the same.
Z-Scores of the COT data can be combined with the Z-Scores of the
close price to accurately pinpoint turning points. But, I would
still detect, verify and interpret a Entry/Exit Trading Signal for
precise timing.
I also modified plots for the following code to indicate whether the
Bands have been crossed, which would warn me to look for a trading
signal, whether a continuation signal or counter-trend
pullback/Breakout signal:
/* Anticipating the next bar BBandBot OR BBandTop Cross, by D.
Tsokakis, Sept 2003. Both crosses come from the same 2nd degree
equation A2*X^2+A1*X+A0=0 The solution is the X2 array. For visual
verification, a pink arrow is plotted when the X2 crosses the next
bar Close AND a red arrow points the actual Cross. */
n=20; f=2;
Qn=Sum(C^2,n);Qn_1=Sum(C^2,n-1);
Sn=Sum(C,n);Sn_1=Sum(C,n-1);
Mn=Sn/n;Mn_1=Sn_1/(n-1);
Kn=(1/n)*sqrt(n*Qn-Sn^2);Kn_1=(1/(n-1))*sqrt((n-1)*Qn_1-Sn_1^2);
bb=Mn-f*Kn;bt=Mn+f*Kn;
S=Sn_1;Q=Qn_1;
A2=(n-1)*(f^2-n+1);
A1=-2*(f^2+1-n)*S;
A0=f^2*n*Q-f^2*S^2-S^2;
x1=(-A1-sqrt(A1^2-4*A2*A0))/(2*A2);
x2=(-A1+sqrt(A1^2-4*A2*A0))/(2*A2);
Plot(C,"C",1,8);
Plot(X1,"",colorBlue,1);
Plot(X2,"",colorBlue,1);Plot(bb,"BBandBot",7,1);Plot
(bt,"BBandTop",7,1);
PlotShapes(shapeUpTriangle*Cross(x2,Ref(C,1)),colorPink);
//PlotShapes(shapeUpArrow*(Cross(bb,C)),colorRed);
PlotShapes(shapeDownTriangle*Cross(Ref(C,1),x1),colorAqua);
//PlotShapes(shapeDownArrow*(Cross(C,bt)),colorBrightGreen);
Title="The next "+Name()+" Close should be "+"\n *below"+WriteVal(x2)
+" for a BBandBot Cross"+
"\n *above"+WriteVal(x1)+" for a BBandTop Cross"+
"\n Actual Next Close = "+WriteIf(Cum(1)!=LastValue(Cum(1)),WriteVal
(Ref(C,1)),"?");
Regards,
Pal
--- In amibroker@xxxxxxxxxxxxxxx, "Gary A. Serkhoshian"
<serkhoshian777@xxxx> wrote:
> Pal,
>
> That makes sense as I've visually seen what you've described. It
seems like our primary job when interpreting the data is to determine
where the critical inflection points are versus noise.
>
> I've worked with Bollinger Bands and the net positions of the three
groups, but am interested in how Z-Score differs from what a
Bollinger Band plots, and does it give a better sense of the
inflection point we seek.
>
> In addition, should any changes be made to the ZScore code as
listed below for non-normal distribution as you describe COT data to
be? How do you determine if the data is normally distributed?
>
> Sorry for all the questions, but you've piqued my interest, and
you've been very clear in your explainations.
>
> I'd be happy to code any adjustments based on your suggestions, and
post them on the board.
>
> Code Below
>
> Kind Regards,
> Gary
>
>
> /*
>
> There is one interpretation of the Z-Score that takes an
observation from a
>
> population and returns a Z-Score statistic, where the Z-Score is a
>
> measurement of the number of standard deviations that that specific
>
> observation deviates from the mean. If this is the interpretation
you
>
> intend, the following afl code returns the Z-Score of the Close of
the most recent 50 days of an end-of-day price series and plots it.
Copy this code and paste it into Indicator Builder.
>
> Note that most of the Closes (95 percent, on average) will have
ZScore
>
> values between -2.0 and +2.0.
>
> */
>
> // ZScore of Close
>
> ZLen = 50;
>
> ZScore = (C-MA(C,ZLen))/StDev(C,ZLen);
>
> Plot(C,"C",colorBlack,style=styleCandle);
>
> Plot(ZScore,"ZScore",colorBlue,styleOwnScale|styleNoLabel,-3,3);
>
> Plot(0,"",colorRed,styleOwnScale|styleNoLabel,-3,3);
>
> Plot(-2.0,"", colorRed,styleOwnScale|styleNoLabel,-3,3 );
>
> Plot(2.0,"", colorRed,styleOwnScale|styleNoLabel,-3,3);
>
> /*
>
> Version 2
>
> normal percentile to Z Score conversion
>
> Schmeiser (1979) came up with the following simple formula for p >
0.5:
>
> z = {p ^ 0.135 - (1-p) ^ 0.135} / 0.1975
>
> According to a table in Shore (1982), it is accurate to two digits
at p = 0, 0.4, 0.8, ...,
>
> which may be good enough.
>
> */
>
> //p = 0.025;
>
> p = Param("p", 0.025, 0.0001, 0.9999, 0.0001 );
>
> pp = IIf(p>=0.5, p, 1.0-p);
>
> z = ((pp ^ 0.135) - ((1.0-pp) ^ 0.135)) / 0.1975;
>
> z = IIf(p>=0.5, z, -z);
>
> //----------------------
>
>
>
>
>
>
>
> palsanand <palsanand@xxxx> wrote:
> Gary,
>
> If you plot the Net Longs of all the 3 players (Commercials, Large
> speculators and Small traders), you will see that the plot of the
> Commercials and Large speculators are at opposite sides about the
> mean (most of the time) and the small traders closer to the mean.
>
> You will see that the plot of the Commercials and Large speculators
> are either diverging from each other or going parallel (most of the
> time).
>
> You can then watch for trend-change pullbacks or breakout signals
at
> the specific time on the plot where the Commercials and Large
> Speculators begin converging from their extreme positions (visually
> identified) on either side of the mean.
>
> You may use Z-Scores to identify the extreme positions. Z-Scores
> tend to be used mainly in the context of the normal curve, and
their
> interpretation based on the standard normal table. It would be
> erroneous to conclude, however, that Z-Scores are limited to
> distributions that approximate the normal curve. Non-normal
> distributions can also be transformed into sets of Z-Scores. In
this
> case the standard normal table cannot be consulted, since the shape
> of the distribution of Z-Scores is the same as that for the
original
> non-normal distribution. For instance, if the original distribution
> is positively skewed the distribution of Z-Scores also will be
> positively skewed.
>
> Regardless of the shape of the distribution, the shift to Z-Scores
> always produces a distribution with a mean of 0 and a variance of 1.
>
> Regards,
>
> Pal
>
> --- In amibroker@xxxxxxxxxxxxxxx, "Gary A. Serkhoshian"
> <serkhoshian777@xxxx> wrote:
> > Pal,
> >
> > Thanks for the post as I've been racking my brain thinking of
ways
> to trade COT. Could you please elaborate on your statement below.
> Specifically, how are you identifying extremes (std dev?), and when
> you write "low points and turning up" are you referring to the net
> commercial position. Taking it a step further, can I assume you
mean
> net-short commerical?
> >
> > Thanks,
> > Gary
> >
> > So, for those places where the
> > Commercials are at extreme low points and turning up, and the
Large
> > speculators are at the opposite extreme and turning down, the
> market
> > will probably turn down shortly (vice-versa for an upside move).
> The
> > small speculators are usually trading with the primary trend.
> >
> >
> >
> >
> > ---------------------------------
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