[amibroker] Exponential Standard Deviation (EStDev)

["liberte721" <liberte@xxxxxxxxxxxxx>]

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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