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I think Ami uses the population Stdev rather than the
sample Stdev. ie.
function edev(P, pds)
{
mean = EMA(p, pds);
dev = sqrt(EMA(P^2, pds) - mean^2);
return dev;
} if you replace ema with ma, the result is the same as stdev.
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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