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Pal,
Great stuff, and thanks for the thorough explaination. If I interpret what you've written below on the mean, the determinant of normal distribution is the number of samples > 30 and size of samples. How big does the sample need to be, and could you provide a practical example with something simple like a moving average?
Thanks for the code. Regarding the two versions of Z Scores listed in my prior e-mail which do you prefer using?
Many thanks in advance, and appreciate you breaking-down these complexities in terms my 10 year-old cousin could understand : )
Warmest,
Gary
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
palsanand <palsanand@xxxxxxxxx> wrote:
Hi,Third attempt...//PlotShapes(shapeUpTriangle*Cross(x2,Ref(C,1)),colorAqua);PlotShapes(shapeUpArrow*(Cross(bb,C)),colorAqua);//PlotShapes(shapeDownTriangle*Cross(Ref(C,1),x1),colorPink);PlotShapes(shapeDownArrow*(Cross(C,bt)),colorRed);It's getting late...Pal--- In amibroker@xxxxxxxxxxxxxxx, "palsanand" <palsanand@xxxx> wrote:> Hi,> > Sorry, here is the correct code:> > PlotShapes(shapeUpTriangle*Cross(x2,Ref(C,1)),colorAqua);> //PlotShapes(shapeUpArrow*(Cross(bb,C)),colorRed);> PlotShapes(shapeDownTriangle*Cross(Ref(C,1),x1),colorPink);> //PlotShapes(shapeDownArrow*(Cross(C,bt)),colorBrightGreen);> > Pal> > --- In amibroker@xxxxxxxxxxxxxxx, "palsanand" <palsanand@xxxx> wrote:> > 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,>> > > > > > 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.> > > > > > > > > > > > > > > > > > > > ---------------------------------> > > > Do you Yahoo!?> > > > Yahoo! SiteBuilder - Free, easy-to-use web site design software> > > > > > > > > Yahoo! Groups SponsorADVERTISEMENT> > > > > > Send BUG REPORTS to bugs@xxxx> > > Send SUGGESTIONS to suggest@xxxx> > > -----------------------------------------> > > Post AmiQuote-related messages ONLY to: amiquote@xxxxxxxxxxxxxxx
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