_SECTION_BEGIN("Cross Prediction");
//Ct is the necessary tomorrows Close for a Ti3a, Ti3b touch.
//One of the most important side effects is the crosses of this Ct with the actual Close : They usually anticipate by 1 Day the Cross(Ti3a,Ti3b).

// Cross(Ti3a,Ti3b) predictions, by D. Tsokakis, April 2004
pa=10;pb=20;//pb should be higher than pa
Plot(C,"C",1,8);
 // Ti3a
sa=0.8;fa=2/(pa+1);
e1a=EMA(C,pa);
e2a=EMA(e1a,pa);
e3a=EMA(e2a,pa);
e4a=EMA(e3a,pa);
e5a=EMA(e4a,pa);
e6a=EMA(e5a,pa);
c1a=-sa*sa*sa;
c2a=3*sa*sa+3*sa*sa*sa;
c3a=-6*sa*sa-3*sa-3*sa*sa*sa;
c4a=1+3*sa+sa*sa*sa+3*sa*sa;
Ti3a=c1a*e6a+c2a*e5a+c3a*e4a+c4a*e3a;
Plot(Ti3a,"Ti3("+WriteVal(pa,1.0)+")",colorBlue,1);
Ga=
(1-fa)*(C1a*fa^5+C2a*fa^4+C3a*fa^3+C4a*fa^2)*e1a+
(1-fa)*(C1a*fa^4+C2a*fa^3+C3a*fa^2+C4a*fa)*e2a+
(1-fa)*(C1a*fa^3+C2a*fa^2+C3a*fa+C4a)*e3a+
(1-fa)*(C1a*fa^2+C2a*fa+C3a)*e4a+
(1-fa)*(C1a*fa+C2a)*e5a+
(1-fa)*(C1a)*e6a;
GGa=C1a*fa^6+C2a*fa^5+C3a*fa^4+C4a*fa^3;
// Ti3b
sb=0.7;fb=2/(pb+1); 
e1b=EMA(C,pb);
e2b=EMA(e1b,pb);
e3b=EMA(e2b,pb);
e4b=EMA(e3b,pb);
e5b=EMA(e4b,pb);
e6b=EMA(e5b,pb);
c1b=-sb*sb*sb;
c2b=3*sb*sb+3*sb*sb*sb;
c3b=-6*sb*sb-3*sb-3*sb*sb*sb;
c4b=1+3*sb+sb*sb*sb+3*sb*sb;
Ti3b=c1b*e6b+c2b*e5b+c3b*e4b+c4b*e3b;
Plot(Ti3b,"Ti3("+WriteVal(pb,1.0)+")",colorRed,1);
Gb=
(1-fb)*(C1b*fb^5+C2b*fb^4+C3b*fb^3+C4b*fb^2)*e1b+
(1-fb)*(C1b*fb^4+C2b*fb^3+C3b*fb^2+C4b*fb)*e2b+
(1-fb)*(C1b*fb^3+C2b*fb^2+C3b*fb+C4b)*e3b+
(1-fb)*(C1b*fb^2+C2b*fb+C3b)*e4b+
(1-fb)*(C1b*fb+C2b)*e5b+
(1-fb)*(C1b)*e6b;
GGb=C1b*fb^6+C2b*fb^5+C3b*fb^4+C4b*fb^3;
Ct=(Gb-Ga)/(GGa-GGb);
Plot(Ct,"Ct",2,1);
// Actual Cross signals
PlotShapes(shapeDownTriangle*Cross(tI3b,tI3a),colorPink);
PlotShapes(shapeUpTriangle*Cross(tI3a,tI3b),colorBlue);
// Prediction signals
PlotShapes(shapeDownArrow*Cross(Ct,C),colorRed);
PlotShapes(shapeUpArrow*Cross(C,Ct),colorBrightGreen);

//The statistics were better than expected:
//for Cross(Ti3(10),Ti3(20)) there was no False Signal for 3815 crosses of the N100 database from Jan2000 till Now.
//for Cross(Ti3(5),Ti3(10)) we have had 8323 crosses without any False Signal !!
//Explore for all quotations with

// False predictions
period1=5;period2=10;// period2 should be higher than period1
Plot(C,"C",1,8);
 // Ti3_10 
pa=period1;sa=0.8;fa=2/(pa+1);
e1a=EMA(C,pa);
e2a=EMA(e1a,pa);
e3a=EMA(e2a,pa);
e4a=EMA(e3a,pa);
e5a=EMA(e4a,pa);
e6a=EMA(e5a,pa);
c1a=-sa*sa*sa;
c2a=3*sa*sa+3*sa*sa*sa;
c3a=-6*sa*sa-3*sa-3*sa*sa*sa;
c4a=1+3*sa+sa*sa*sa+3*sa*sa;
Ti3a=c1a*e6a+c2a*e5a+c3a*e4a+c4a*e3a;
Plot(Ti3a,"Ti3a",colorBlue,1);
Ga=
(1-fa)*(C1a*fa^5+C2a*fa^4+C3a*fa^3+C4a*fa^2)*e1a+
(1-fa)*(C1a*fa^4+C2a*fa^3+C3a*fa^2+C4a*fa)*e2a+
(1-fa)*(C1a*fa^3+C2a*fa^2+C3a*fa+C4a)*e3a+
(1-fa)*(C1a*fa^2+C2a*fa+C3a)*e4a+
(1-fa)*(C1a*fa+C2a)*e5a+
(1-fa)*(C1a)*e6a;
GGa=C1a*fa^6+C2a*fa^5+C3a*fa^4+C4a*fa^3;
// Ti3_20
pb=period2;sb=0.7;fb=2/(pb+1);//pb should be higher than pa
e1b=EMA(C,pb);
e2b=EMA(e1b,pb);
e3b=EMA(e2b,pb);
e4b=EMA(e3b,pb);
e5b=EMA(e4b,pb);
e6b=EMA(e5b,pb);
c1b=-sb*sb*sb;
c2b=3*sb*sb+3*sb*sb*sb;
c3b=-6*sb*sb-3*sb-3*sb*sb*sb;
c4b=1+3*sb+sb*sb*sb+3*sb*sb;
Ti3b=c1b*e6b+c2b*e5b+c3b*e4b+c4b*e3b;
Plot(Ti3b,"Ti3b",colorRed,1);
Gb=
(1-fb)*(C1b*fb^5+C2b*fb^4+C3b*fb^3+C4b*fb^2)*e1b+
(1-fb)*(C1b*fb^4+C2b*fb^3+C3b*fb^2+C4b*fb)*e2b+
(1-fb)*(C1b*fb^3+C2b*fb^2+C3b*fb+C4b)*e3b+
(1-fb)*(C1b*fb^2+C2b*fb+C3b)*e4b+
(1-fb)*(C1b*fb+C2b)*e5b+
(1-fb)*(C1b)*e6b;
GGb=C1b*fb^6+C2b*fb^5+C3b*fb^4+C4b*fb^3;
Ct=(Gb-Ga)/(GGa-GGb);
Plot(Ct,"Ct",2,1);
PlotShapes(shapeDownTriangle*Cross(tI3b,tI3a),colorPink);
PlotShapes(shapeDownArrow*Cross(Ct,C),colorRed);
PlotShapes(shapeUpTriangle*Cross(tI3a,tI3b),colorBlue);
PlotShapes(shapeUpArrow*Cross(C,Ct),colorBrightGreen);
PredictionDN=Cross(Ct,C);PredictionUP=Cross(C,Ct);
CrossDN=Cross(Ti3b,Ti3a);CrossUP=Cross(Ti3a,Ti3b);
Filter=CrossDN OR CrossUP;
AddColumn(PredictionDN,"0barsDN",1.0);
AddColumn(Ref(PredictionDN,-1),"1barDN",1.0);
AddColumn(Ref(PredictionDN,-2),"2barsDN",1.0);
AddColumn(CrossDN AND NOT(predictionDN OR Ref(predictionDN,-1) OR Ref(predictionDN,-2)),"FalseUP",1.0);
AddColumn(PredictionUP,"0barsUP",1.0);
AddColumn(Ref(PredictionUP,-1),"1barUP",1.0);
AddColumn(Ref(PredictionUP,-2),"2barsUP",1.0);
AddColumn(CrossUP AND NOT(predictionUP OR Ref(predictionUP,-1) OR Ref(predictionUP,-2)),"FalseDN",1.0);


_SECTION_END();