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Hi Dan,
Try using a Hull MA -- it's a lot faster.
Peace and Justice --- Patrick
----- Original Message -----
Sent: Sunday, May 21, 2006 8:42 PM
Subject: [amibroker] Exponential Standard
Deviation (EStDev)
Trying to figure out volatility, I had an interesting diversion
into
what StDev is doing, and how I might make something more useful.
Since StDev uses a simple moving average in its calculation, you'll
see a laggy bounce effect from sudden price changes. That is the way
it is defined, and that is fine, but not what I wanted. So I swapped
out the MA for EMA, and I like the result.
dan
/*
Exponential Standard Deviation
by Daniel LaLiberte
liberte@xxxxxxxxxxxxx
Same calculation as Standard Deviation,
but
using an EMA instead of MA. The effect is to smooth
out the
laggy bounce from sudden changes.
For comparision, I tried to reproduce
the built-in StDev function,
and discovered that it is using a rapid
calculation method instead.
The RapidStDev function defined below appears
to work just like
StDev,
although there my be some rounding errors, or
perhaps a different
method
is actually used. It would be good for
this to be documented.
The standard (non-rapid) form of the calculation
is described at:
http://stockcharts.com/education/IndicatorAnalysis/indic_standardDev.h
tml
Wikipedia
tells all: http://en.wikipedia.org/wiki/Standard_deviation
Also
see comparison of different methods for AmiBroker:
http://www.purebytes.com/archives/amibroker/2005/msg01812.html
Using
the standard form of the standard deviation, I modified
it to use an
exponential moving average instead of the normal MA.
This is EStDev.
I also modified RapidStDev to create an
expontial form, RapidEStDev.
Curiously, the two functions perform
identically, for large enough
n.
*/
function EStDev(base, n)
{
// Calculate the simple
average (mean) of the closing price.
// Use EMA instead, to de-bounce the
spikes
// m = MA(base, n); //
orignial
m = EMA(base, n); //
exponential
// subtract the average closing price from the actual
closing price.
d = m - base;
//
Square each period's deviation.
d2 = d *
d;
// Sum the squared deviations.
// Divide that by the number of
periods.
// sd2 = MA(d2, n); //
original
sd2 = EMA(d2, n); //
exponential
// The StDev is then equal to the square root of that
number.
sd =
sqrt(sd2);
return sd;
}
function RapidStDev(base,
n)
{
m = MA(base,
n);
return Sqrt( (Sum(base * base, n) - n *
m * m ) / (n - 1) );
}
function RapidEStDev(base,
n)
{
m = EMA(base,
n);
return Sqrt( (n * EMA(base * base, n) -
n * m * m ) / (n -
1) );
}
pds = Param("pds", 200, 2, 500,
1);
// These two are the same:
Plot(EStDev(Close, pds), "EStDev",
colorBlack);
Plot(RapidEStDev(Close, pds), "RapidEStDev",
colorRed);
// These two are the same:
Plot(StDev(Close, pds),
"StDev", colorBlue);
Plot(RapidStDev(Close, pds), "RapidStDev",
colorGold);
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