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PS.Convexity and Concavity are widely used in the holy target to
make money.
See for example
http://cepa.newschool.edu/het/essays/uncert/aversion.htm
http://chinook.gsia.cmu.edu/investments-day/lecture11-2001.pdf
http://www.contingencyanalysis.com/measureduration.htm
I think this approach is beyond the scopes of this list and I hope
you will agree...
Dimitris Tsokakis
--- In amibroker@xxxxxxxxxxxxxxx, "Dimitris Tsokakis" <TSOKAKIS@xxxx>
wrote:
> An ideal sinusoidal has 4 phases:
>
> Convex AND Ascending;// colorDarkGreen
> Concave AND Ascending;// colorTurquoise
> Concave AND Descending;// colorDarkRed
> Convex AND Descending;// colorPink
> The IB code illustrates the example
>
> // The 4 phases of an ideal sinusoidal
> freq = 1;
> y=sin( Cum( freq/10 ) );
> t=1;
> Convex=(y-Ref(y,-t))/t>=(y-Ref(y,-(t+1)))/(t+1);
> Concave=NOT(Convex);
> Ascending=y>=Ref(y,-1);
> Descending=NOT(ascending);
> Bullstart=Convex AND Ascending;
> Bullend=Concave AND ascending;
> Bearstart=Concave AND Descending;
> Bearend=Convex AND Descending;
> Color=IIf(Bullstart,colorDarkGreen,IIf(Bullend,colorTurquoise,IIf
(Bearstart,colorDarkRed,colorPink)));
> Plot(y,"",Color,8);
>
> [see sin.gif]
> We shall use a smoothing procedure [IIR2 filter] as close to the
sinusoidal as possible. [see IIR2.gif]
> Of course the trend characteristics do not give the [-1, +1]
oscillation, but the convexity/concavity are still detectable.
> The superimpose of actual price candles gives a more descriptive
picture of the 4 phases.
> [see 4phases.gif]
> The full code is
>
> // The 4 phases of a stock graph
> // A. Smothing procedure
> function IIR2( input, f0, f1, f2 )
> {
> result[ 0 ] = input[ 0 ];result[ 1 ] = input[ 1 ];
> for( i = 2; i < BarCount; i++ )
> {
> result[ i ] = f0 * input[ i ] + f1 * result[ i - 1 ] + f2 * result[
i - 2 ];
> }
> return result;
> }
> C1=C;
> k=0.3;
> RD=IIR2( C1, 0.3, 1.2+K, -0.5-K);
> // B. Convexity definition
> y=RD;
> t=1;
> Convex=(y-Ref(y,-t))/t>=(y-Ref(y,-(t+1)))/(t+1);
> Concave=NOT(Convex);
> Ascending=y>=Ref(y,-1);
> Descending=NOT(ascending);
> // C. Trend phases
> Bullstart=Convex AND Ascending;// from A to B
> Bullend=Concave AND ascending;// from B to C
> Bearstart=Concave AND Descending;// from C to D
> Bearend=Convex AND Descending;// from D to E
> // D. Application
> Color=IIf(Bullstart,colorDarkGreen,IIf(Bullend,colorTurquoise,IIf
(Bearstart,colorDarkRed,colorPink)));
> Plot(y,"",Color,8+styleThick);
> Plot(C,"",47,64);GraphXSpace=5;
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