The last best-fit IIR2 does not give the solutions the last best-fit parabolic can give
In the following code I calculate the IIR2 coefficient K for the
IIR2( C1, 0.3, 1.2+K, -0.5-K);
in a reasonable range from -0.5 to +0.5, keeping af0=0.3 to avoid undesirable oscillations.
// The last best-fit parabolic vs the best-fit IIR2, by D. Tsokakis, Sept2004
Plot(C,"C",1,64);
perc=3;//sensitivity calibration
x=BarIndex();xx=LastValue(x);
t1=LastValue(ValueWhen(PeakBars(H,perc)==0,x));
H1=LastValue(ValueWhen(PeakBars(H,perc)==0,H));
t11=LastValue(ValueWhen(TroughBars(L,perc)==0,x));
H11=LastValue(ValueWhen(TroughBars(L,perc)==0,L));
g=t1>t11;
shape=IIf(g,shapeDownArrow*(x==t1),shapeUpArrow*(x==t11));
Color=IIf(g,colorRed,colorBrightGreen);
PlotShapes(shape,color);
// 1. THE LAST BEST-FIT PARABOLIC
t=IIf(g,x-t1,x-t11);
diff1=IIf(g,H1*(xx-t1),H11*(xx-t11));
Lma=LastValue(MA(C,50));
f1=0;f2=IIf(Lma<100,1,0)+3*int(log10(Lma));
fa=0;fb=0;step=f2/100;
for(f=f1;f<f2;f=f+step)
{
parabolic=IIf(g,H1-f*t^2,H11+f*t^2);
S1=LastValue(Sum(abs(parabolic-H),xx-t1));
S11=LastValue(Sum(abs(parabolic-L),xx-t11));
diff=IIf(g,S1,S11);
if(diff<diff1)
{
diff1=diff;fa=f;
}
}
for(f=Max(fa-step,0);f<fa+step;f=f+0.01*step)
{
parabolic=IIf(g,H1-f*t^2,H11+f*t^2);
S1=LastValue(Sum(abs(parabolic-H),xx-t1));
S11=LastValue(Sum(abs(parabolic-L),xx-t11));
diff=IIf(g,S1,S11);
if(diff<diff1)
{
diff1=diff;fb=f;
}
}
p=IIf(g,H1-fb*t^2,H11+fb*t^2);
Plot(IIf(x>=Max(t1,t11),p,-1e10),"",color,8);
//THE LAST BEST-FIT IIR2
function IIR2( input, af0, af1, af2 )
{
result[ 0 ] = input[ 0 ];result[ 1 ] = input[ 1 ];
for( i = 2; i < BarCount; i++ )
{
result[ i ] = af0 * input[ i ] + af1 * result[ i - 1 ] + af2 * result[ i - 2 ];
}
return result;
}
PER=IIf(g,xx-t1,xx-t11);
C1=IIf(g,H,L);DIF1=10000;
K0=-0.5;K00=0.5;STEP=0.01;
for(K=K0;K<K00;K=K+STEP)
{
RED=IIR2( C1, 0.3, 1.2+K, -0.5-K);
dif=LastValue(Sum(abs(RED-C1),PER));
if(DIF<DIF1)
{
K1=K;
DIF1=DIF;
}
}
BESTFIT_IIR2=IIR2(C1,0.3,1.2+K1,-0.5-K1);
Plot(IIf(X>=Max(t1,t11),BESTFIT_IIR2,Null),"",colorYellow,8);
Title=Name()+
", "+WriteIf(t1>t11,"f_desc","f_asc")+"="+
WriteVal(fb,1.4)+",K_"+WriteIf(t1>t11,"desc","asc")+"="+WriteVal(k1);
GraphXSpace=3;
If the stock is still ascending[descending] since the last trough[peak], the comparison is probably interesting.
[^VXO graph]
If minor troughs[peaks] have already occurred, then the correlation does not make sense, the IIR2 in no more monotonous.
[QQQ graph]
