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Andrew,
I had a quick look at it. I have such a jump going from 14 to 15
March 2001, but did not bother to check the rest. It is a rolling
formula, using the previous 50 days to calculate, and I suspect that,
if you go 50 days back from the date of the kurtosis jump, you'll get
a huge jump in the index itself, that now worked itself out of the
system.
I've checked the exact formula against some stat package and it
tallies to the xth decimal. The approx is not that accurate, so it
could be due to the way the approx works as well. But I think it is
mostly a huge data jump. Look at the following
-1 +1 -1 +1 -1 +1 -1 +1 -20 +50 -1 +1 -1 +1 -1 +1
This series will have a huge jump in kurtosis around the middle
when you see those two huge return figures, but, depending on the
kurtosis length, will return suddenly to normal the moment those
two big figures work themselves out of the system. Note that those
two jumps would favour a net bought option position over the life
of the series, to give away some of our system.
To fix it, use a longer time period, such as 150. It smoothes it
out a bit.
Regards
MG Ferreira
TsaTsa EOD Programmer and trading model builder
http://tsatsaeod.ferra4models.com
http://www.ferra4models.com
--- In equismetastock@xxxxxxxxxxxxxxx, "Andrew Tomlinson"
<andrew_tomlinson@xxxx> wrote:
>
> MG
>
> If I apply your approximate kurtosis formula (50 days) to the NDX, I get
> some disconcerting discontinuities - e.g. 3/15/01 5.8 3/16/01 -0.71,
> similarly Jan 2002 and Dec 1999. The exact formula can't go to 50
days, but
> has similar jumps. My statistics are rusty, but I would not expect
to see
> such bar to bar jumps in these series. What am I missing?
>
> Andrew
>
>
>
> -----Original Message-----
> From: MG Ferreira [mailto:quant@x...]
> Sent: Friday, March 04, 2005 11:08 AM
> To: equismetastock@xxxxxxxxxxxxxxx
> 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<-----------------------------------------------------
>
>
>
>
>
>
>
> Yahoo! Groups Links
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