Quantitative Trading Systems

//	StandardDeviationSinglePass.afl
//
//	A function to compute the standard deviation
//	of a price series in a single pass.
//	AmiBroker implementation by Howard Bandy
//	www.BlueOwlPress.com
//	November 2011
//

function SDSP( p, LB )
{
//	p is the price series beign processed
//	LB is the number of bars in the lookback period
//	for the calculation of the standard deviation

    if ( LB <= 1 )
    {
        //	set standard deviation to zero
        //	if the lookback period is too short
        //	to give meaningful results.
        Std = 0;
    }
    else
    {
        for ( i = 0; i < LB; i++ )
        {
            //	set std dev to zero for the
            //	bars in the rampup period
            Std[i] = 0;
        }

        for ( i = LB; i < BarCount; i++ )
        {
            //	compute the std dev for all bars
            //	for each element
            //	k runs from 1 through LB

            //	k = 1
            x = p[i-LB+1];
            mo = x;
            so = 0;
            //	k = 2 through LB

            for ( k = 2; k <= LB; k++ )
            {
                x = p[i-LB+k];
                mn = mo + ( x - mo ) / k;
                sn = so + ( x - mo ) * ( x - mn );
                mo = mn;
                so = sn;
            }	//	end for k loop

            //	for the ith element --
            //	mo holds the mean (which is not returned)
            //	so holds the sum of squared differences
            //	used to compute the variance.
            //	Divide by LB to get the population variance,
            //	of by (LB-1) to get the sample variance.
            Var = so / LB;

            //	standard deviation is the square root of the variance
            Std[i] = sqrt( Var );
        }	//	end for i loop
    }

    return( Std );
}	// end of function SDSP

//	Program to compute and plot the
//	standard deviation using two methods.
//

//	Plot the candlesticks of price
Plot( C, "C", colorBlack, styleCandle );

//	Set the length
LB = 10;

//	Use the method built in to AmiBroker
//	and plot it as a green line
SDBuiltin = StDev( C, LB );
Plot( SDBuiltIn, "SDBI", colorGreen, styleLine | styleOwnScale, -1, 3 );

//	Use the function
//	and plot it as a red line
SDSPass = SDSP( C, LB );
Plot( SDSPass, "SDSPass", colorRed, styleLine | styleOwnScale, -1, 3 );

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