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I am not sure I understand you corretly, but there is a standard
formula for kurtosis, which is the 'exact' one I gave. The 'approx'
is a lot easier to use in practise and can go back much further
(longer period). You can not implement the 'exact' in that way in MS
as far as I know, after about 20 periods you get some funny error,
so that is why there is an approx in the first place.
I *think* dusant's formula measures the same thing, ie has the
same idea in it, but it is not the official kurtosis formula, if
there is such as an official formula.
Regards
MG Ferreira
TsaTsa EOD Programmer and trading model builder
http://tsatsaeod.ferra4models.com
http://www.ferra4models.com
--- In equismetastock@xxxxxxxxxxxxxxx, "cardiop" <cardiop@xxxx> wrote:
>
> MG Ferreira and Dusant...
>
> Friends...
> You presented two formulate for Kurtosis... formulate Them
> different and take the different graphs. What she would be
> formulates it exata?
> Thank you
> Skill
>
>
>
>
>
>
>
> > Do we need such a complex code for Kurtosis?
> >
> > Mov( Mov( Mo( 4) - Ref( Mo( 4), -1), 50, E), 10, S)
> >
> > should do ... or substitute the 4, 50, 10 for any values
> > which you feel is good.
> >
> > Dusant
> > ----- Original Message -----
> > From: MG Ferreira
> > To: equismetastock@xxxx
> > Sent: Friday, March 04, 2005 9:37 PM
> > Subject: [EquisMetaStock Group] Skewness or biasedness
> > and kurtosis
> >
> >
> >
> > Herewith code for the skewness and kurtosis of a series
> > (somebody requested this, so don't jump to conclusions -
> > specifically, don't test this as a trading model -
> > caveat emptor - This is often useful when trading
> > options and we used these things to devise option
> > strategies, such as building indicators that tell you if
> > you should be buying/writing puts or calls, in or out
> > the money etc - but - don't be mislead by this statement
> > as these are the basic building blocks of such a system,
> > not the system itself - and given upon request...)
> >
> > It is a bit troublesome to do this in Metastock due to
> > the way in which its time series processor works. You
> > have to manually add up the history to get the exact
> > version, but you can easily build a good approximation.
> > The exact version quickly causes Metastock to give an
> > error message, and we limit it to 20 days, which really
> > is too little for this indicator. We also give an
> > approximate version which is very easy to code and use,
> > and here you can go much higher than the 20 day limit of
> > the exact system. The exact system also shows how you
> > can use boolean algebra in stead of lots of if
> > statements. Typically you should have a highish value for
> > these, say 50 and above.
> >
> > OK, so there are four formulas in total, exact and
> > approximate ones for the skewness or bias and the
> > kurtosis. Note that we calculate, as you should, these
> > figures in the return series, not the series itself.
> >
> > How do you interpret these? Just a brief summary.
> >
> > Skewness: If this is positive, then the market has a
> > positive news impact curve. Up movements are generally
> > higher than down movements. If this value is negative,
> > then vice versa. Here is an example of movements in a
> > positive skew market:
> >
> > +2 -1 +5 -3 +3 -1 +3 -1 +2
> >
> > Note that, if the market rises, it generally rises more
> > than if it falls.
> >
> > Kurtosis: If this value is positive, it means the
> > returns are leptokurtic. A negative value indicates a
> > platykurtic distribution. Leptokurtic technically means
> > there are more outliers than in a normal distribution,
> > in practise it is indicative of a risky market. The
> > higher this value, the more risky the market is, with 0
> > sort of meaning it is a normal market. A low value means
> > that you have a low risk market. Here is an example of
> > a leptokurtic market:
> >
> > +1 -1 +1 -1 +10 -1 +1 -1 +12 -2 +1 -1 +2 -1
> >
> > Note that the market's return is quite concentrated
> > around zero but every now and again you have a HUGE
> > outlier - this is leptokurtosis.
> >
> > Code follows below, note it is in four sections.
> >
> > Regards
> > MG Ferreira
> > TsaTsa EOD Programmer and trading model builder
> > http://tsatsaeod.ferra4models.com
> > http://www.ferra4models.com
> >
> > ----------8<----------------------------------------------
> > ------- {Bias Exact Metastock code
> > -------------------------
> > MG Ferreira
> > http://www.ferra4models.com
> > For personal use only}
> >
> > xx := INDICATOR;
> > ll := Input("Bias length:",1,20,20);
> > yy := ROC(xx,1,%);
> > mm := Mov(yy,ll,S);
> > ss := Power(yy-mm,3)+
> > Power((Ref(yy,-1)-mm)*(ll>1),3)+
> > Power((Ref(yy,-2)-mm)*(ll>2),3)+
> > Power((Ref(yy,-3)-mm)*(ll>3),3)+
> > Power((Ref(yy,-4)-mm)*(ll>4),3)+
> > Power((Ref(yy,-5)-mm)*(ll>5),3)+
> > Power((Ref(yy,-6)-mm)*(ll>6),3)+
> > Power((Ref(yy,-7)-mm)*(ll>7),3)+
> > Power((Ref(yy,-8)-mm)*(ll>8),3)+
> > Power((Ref(yy,-9)-mm)*(ll>9),3)+
> > Power((Ref(yy,-10)-mm)*(ll>10),3)+
> > Power((Ref(yy,-11)-mm)*(ll>11),3)+
> > Power((Ref(yy,-12)-mm)*(ll>12),3)+
> > Power((Ref(yy,-13)-mm)*(ll>13),3)+
> > Power((Ref(yy,-14)-mm)*(ll>14),3)+
> > Power((Ref(yy,-15)-mm)*(ll>15),3)+
> > Power((Ref(yy,-16)-mm)*(ll>16),3)+
> > Power((Ref(yy,-17)-mm)*(ll>17),3)+
> > Power((Ref(yy,-18)-mm)*(ll>18),3)+
> > Power((Ref(yy,-19)-mm)*(ll>19),3);
> > ll*ss/(Power(Stdev(yy
> > ,ll)*Sqrt(ll/(ll-1)),3)*(ll-1)*(ll-2))
> > ----------8<----------------------------------------------
> > ------- {Bias Approx Metastock code
> > --------------------------
> > MG Ferreira
> > http://www.ferra4models.com
> > For personal use only}
> >
> > xx := INDICATOR;
> > ll := Input("Bias length:",1,9999,50);
> > yy := ROC(xx,1,%);
> > mm := Mov(yy,ll,S);
> > dd := yy-mm;
> > ll*Sum(Power(dd,3),ll)/(Power(Stdev(yy
> > ,ll)*Sqrt(ll/(ll-1)),3)*(ll-1)*(ll-2))
> > ----------8<----------------------------------------------
> > ------- {Kurtosis Exact Metastock code
> > -----------------------------
> > MG Ferreira
> > http://www.ferra4models.com
> > For personal use only}
> >
> > xx := INDICATOR;
> > ll := Input("Kurtosis length:",1,20,20);
> > yy := ROC(xx,1,%);
> > mm := Mov(yy,ll,S);
> > ss := Power(yy-mm,4)+
> > Power((Ref(yy,-1)-mm)*(ll>1),4)+
> > Power((Ref(yy,-2)-mm)*(ll>2),4)+
> > Power((Ref(yy,-3)-mm)*(ll>3),4)+
> > Power((Ref(yy,-4)-mm)*(ll>4),4)+
> > Power((Ref(yy,-5)-mm)*(ll>5),4)+
> > Power((Ref(yy,-6)-mm)*(ll>6),4)+
> > Power((Ref(yy,-7)-mm)*(ll>7),4)+
> > Power((Ref(yy,-8)-mm)*(ll>8),4)+
> > Power((Ref(yy,-9)-mm)*(ll>9),4)+
> > Power((Ref(yy,-10)-mm)*(ll>10),4)+
> > Power((Ref(yy,-11)-mm)*(ll>11),4)+
> > Power((Ref(yy,-12)-mm)*(ll>12),4)+
> > Power((Ref(yy,-13)-mm)*(ll>13),4)+
> > Power((Ref(yy,-14)-mm)*(ll>14),4)+
> > Power((Ref(yy,-15)-mm)*(ll>15),4)+
> > Power((Ref(yy,-16)-mm)*(ll>16),4)+
> > Power((Ref(yy,-17)-mm)*(ll>17),4)+
> > Power((Ref(yy,-18)-mm)*(ll>18),4)+
> > Power((Ref(yy,-19)-mm)*(ll>19),4);
> > ll*(ll+1)*ss/(Power(Stdev(yy
> > ,ll)*Sqrt(ll/(ll-1)),4)*(ll-1)*(ll-2)*(ll-3))-3*(ll-1)*(ll
> > -1)/((ll-2)*(ll-3))
> > ----------8<----------------------------------------------
> > ------- {Kurtosis Approx Metastock code
> > ------------------------------
> > MG Ferreira
> > http://www.ferra4models.com
> > For personal use only}
> >
> > xx := INDICATOR;
> > ll := Input("Kurtosis length:",1,9999,50);
> > yy := ROC(xx,1,%);
> > mm := Mov(yy,ll,S);
> > dd := yy - mm;
> > ll*(ll+1)*Sum(Power(dd,4),ll)/(Power(Stdev(yy
> > ,ll)*Sqrt(ll/(ll-1)),4)*(ll-1)*(ll-2)*(ll-3))-3*(ll-1)*(ll
> > -1)/((ll-2)*(ll-3))
> > ----------8<----------------------------------------------
> > -------
> >
> >
> >
> >
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