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This is the finished formula of the Hurst Constant with
interpretation but there could be more to the indicator that this.
With the help of members like Jose, Carlos, MG Ferreira, and PJ
Chai.. This formula seems to work well with the rest of Chaos
analysis. If I left any other contributors to this formula I
apologize.
Kev S.
{Hurst Constant}
prd1:=Input("Periods",60,9999,60);
Bars:=LastValue(Min(prd1,LastValue(Cum(1))));
FR1:=Log(Sum(Abs(C-Ref(C,-1)),Bars));
FR2:=Log(Sum(If((Cum(1)/2-Int(Cum(1)/2))=0,Abs(C-Ref(C,-
2)),0),Bars));
FR3:=Log(Sum(If((Cum(1)/3-Int(Cum(1)/3))=0,Abs(C-Ref(C,-
3)),0),Bars));
FR4:=Log(Sum(If((Cum(1)/4-Int(Cum(1)/4))=0,Abs(C-Ref(C,-
4)),0),Bars));
FR5:=Log(Sum(If((Cum(1)/5-Int(Cum(1)/5))=0,Abs(C-Ref(C,-
5)),0),Bars));
FR6:=Log(Sum(If((Cum(1)/6-Int(Cum(1)/6))=0,Abs(C-Ref(C,-
6)),0),Bars));
FR10:=Log(Sum(If((Cum(1)/10-Int(Cum(1)/10))=0,Abs(C-Ref(C,-
10)),0),Bars));
FR20:=Log(Sum(If((Cum(1)/20-Int(Cum(1)/20))=0,Abs(C-Ref(C,-
20)),0),Bars));
FR30:=Log(Sum(If((Cum(1)/30-Int(Cum(1)/30))=0,Abs(C-Ref(C,-
30)),0),Bars));
FR40:=Log(Sum(If((Cum(1)/40-Int(Cum(1)/40))=0,Abs(C-Ref(C,-
40)),0),Bars));
FR50:=Log(Sum(If((Cum(1)/50-Int(Cum(1)/50))=0,Abs(C-Ref(C,-
50)),0),Bars));
FR60:=Log(Sum(If((Cum(1)/60-Int(Cum(1)/60))=0,Abs(C-Ref(C,-
60)),0),Bars));
SOMXY:=FR2*Log(2)+FR3*Log(3)+FR4*Log(4)+FR5*Log(5)+FR6*Log(6)
+FR10*Log(10)+FR20*Log(20)+FR30*Log(30) +FR40*Log(40)+FR50*Log(50)
+FR60*Log(60);
SOMX:=Log(2)+Log(3)+Log(4)+Log(5)+Log(6)+Log(10)+Log(20)+Log(30)+Log
(40)+Log(50)+Log(60);
SOMY:=FR1+FR2+FR3+FR4+FR5+FR6+FR10+FR20+FR30+FR40+FR50+FR60;
SOMX2:=(Power(Log(2),2))+(Power(Log(3),2))+(Power(Log(4),2))+(Power
(Log(5),2))+(Power(Log(6),2))+(Power(Log(10),2))+(Power(Log(20),2))+
(Power(Log(30),2))+(Power(Log(40),2))+(Power(Log(50),2))+(Power(Log
(60),2));
HURST:=1+((12*SOMXY-SOMX*SOMY)/(12*SOMX2-Power(SOMX,2)));
LIM:=LastValue(Cum(HURST)/(Cum(1)-Bars-60));
HURST;
LIM;
50;
{End}
Hurst used the coefficient as an index for the persistence of the
time series considered. For , it is positively persistent and
characterized by `long memory' effects, as described in the next
section. A rather informal interpretation of used by practitioners
is this: may be interpreted as the chance of movements with the
same sign, Peters (1994). For , it is more likely that an upward
movement is followed by a movement of the same (positive) sign, and
a downward movement is more likely to be followed by another
downward movement. For , a downward movement is more likely to be
reversed by an upward movement thus implying the reverting behavior.
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