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Adaptive Trends And Oscillators

Formula for: MetaStock

Views: 1726

Added: December 04, 2006

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H cycle count 1a
value:= Fml("Hilbert cycle period - 1a");
If(Sum(value,6)>=360 AND Sum(value,5)<360 ,6,0) +
If(Sum(value,7)>=360 AND Sum(value,6)<360 ,7,0) +
If(Sum(value,8)>=360 AND Sum(value,7)<360 ,8,0) +
If(Sum(value,9)>=360 AND Sum(value,8)<360 ,9,0) +
If(Sum(value,10)>=360 AND Sum(value,9)<360 ,10,0) +
If(Sum(value,11)>=360 AND Sum(value,10)<360 ,11,0) +
If(Sum(value,12)>=360 AND Sum(value,11)<360 ,12,0) +
If(Sum(value,13)>=360 AND Sum(value,12)<360 ,13,0) +
If(Sum(value,14)>=360 AND Sum(value,13)<360 ,14,0) +
If(Sum(value,15)>=360 AND Sum(value,14)<360 ,15,0)

H cycle count 2a

value:= Fml("Hilbert cycle period - 1a");
If(Sum(value,16)>=360 AND Sum(value,15)<360 ,16,0) +
If(Sum(value,17)>=360 AND Sum(value,16)<360 ,17,0) +
If(Sum(value,18)>=360 AND Sum(value,17)<360 ,18,0) +
If(Sum(value,19)>=360 AND Sum(value,18)<360 ,19,0) +
If(Sum(value,20)>=360 AND Sum(value,19)<360 ,20,0) +
If(Sum(value,21)>=360 AND Sum(value,20)<360 ,21,0) +
If(Sum(value,22)>=360 AND Sum(value,21)<360 ,22,0) +
If(Sum(value,23)>=360 AND Sum(value,22)<360 ,23,0) +
If(Sum(value,24)>=360 AND Sum(value,23)<360 ,24,0) +
If(Sum(value,25)>=360 AND Sum(value,24)<360 ,25,0)

H cycle count 3a
value:= Fml("Hilbert cycle period - 1a");
If(Sum(value,26)>=360 AND Sum(value,25)<360 ,26,0) +
If(Sum(value,27)>=360 AND Sum(value,26)<360 ,27,0) +
If(Sum(value,28)>=360 AND Sum(value,27)<360 ,28,0) +
If(Sum(value,29)>=360 AND Sum(value,28)<360 ,29,0) +
If(Sum(value,30)>=360 AND Sum(value,29)<360 ,30,0) +
If(Sum(value,31)>=360 AND Sum(value,30)<360 ,31,0) +
If(Sum(value,32)>=360 AND Sum(value,31)<360 ,32,0) +
If(Sum(value,33)>=360 AND Sum(value,32)<360 ,33,0) +
If(Sum(value,34)>=360 AND Sum(value,33)<360 ,34,0) +
If(Sum(value,35)>=360 AND Sum(value,34)<360 ,35,0)

H ip sum 1
pd:=Int(Fml("Hilbert cycle period - final-a"));
pr:=(H+L)/2;
(Cos(0)*pr)+
(Cos(360*(1/pd))*Ref(pr,-1))+
(Cos(360*(2/pd))*Ref(pr,-2))+
(Cos(360*(3/pd))*Ref(pr,-3))+
(Cos(360*(4/pd))*Ref(pr,-4))+
(Cos(360*(5/pd))*Ref(pr,-5))+
If(pd>6, Cos(360*(6/pd))*Ref(pr,-6), 0)+
If(pd>7, Cos(360*(7/pd))*Ref(pr,-7), 0)+
If(pd>8, Cos(360*(8/pd))*Ref(pr,-8), 0)+
If(pd>9, Cos(360*(9/pd))*Ref(pr,-9), 0)+
If(pd>10, Cos(360*(10/pd))*Ref(pr,-10), 0)+
If(pd>11, Cos(360*(11/pd))*Ref(pr,-11), 0)+
If(pd>12, Cos(360*(12/pd))*Ref(pr,-12), 0)+
If(pd>13, Cos(360*(13/pd))*Ref(pr,-13), 0)+
If(pd>14, Cos(360*(14/pd))*Ref(pr,-14), 0)

H ip sum 2

pd:=Int(Fml("Hilbert cycle period - final-a"));
pr:=(H+L)/2;
If(pd>15, Cos(360*(15/pd))*Ref(pr,-15), 0)+
If(pd>16, Cos(360*(16/pd))*Ref(pr,-16), 0)+
If(pd>17, Cos(360*(17/pd))*Ref(pr,-17), 0)+
If(pd>18, Cos(360*(18/pd))*Ref(pr,-18), 0)+
If(pd>19, Cos(360*(19/pd))*Ref(pr,-19), 0)+
If(pd>20, Cos(360*(20/pd))*Ref(pr,-20), 0)+
If(pd>21, Cos(360*(21/pd))*Ref(pr,-21), 0)+
If(pd>22, Cos(360*(22/pd))*Ref(pr,-22), 0)+
If(pd>23, Cos(360*(23/pd))*Ref(pr,-23), 0)+
If(pd>24, Cos(360*(24/pd))*Ref(pr,-24), 0)

H ip sum 3
pd:=Int(Fml("Hilbert cycle period - final-a"));
pr:=(H+L)/2;
If(pd>25, Cos(360*(25/pd))*Ref(pr,-25), 0)+
If(pd>26, Cos(360*(26/pd))*Ref(pr,-26), 0)+
If(pd>27, Cos(360*(27/pd))*Ref(pr,-27), 0)+
If(pd>28, Cos(360*(28/pd))*Ref(pr,-28), 0)+
If(pd>29, Cos(360*(29/pd))*Ref(pr,-29), 0)+
If(pd>30, Cos(360*(30/pd))*Ref(pr,-30), 0)+
If(pd>31, Cos(360*(31/pd))*Ref(pr,-31), 0)+
If(pd>32, Cos(360*(32/pd))*Ref(pr,-32), 0)+
If(pd>33, Cos(360*(33/pd))*Ref(pr,-33), 0)+
If(pd>34, Cos(360*(34/pd))*Ref(pr,-34), 0)

H rp sum 1
pd:=Int(Fml("Hilbert cycle period - final-a"));
pr:=(H+L)/2;
(Sin(0)*pr)+
(Sin(360*(1/pd))*Ref(pr,-1))+
(Sin(360*(2/pd))*Ref(pr,-2))+
(Sin(360*(3/pd))*Ref(pr,-3))+
(Sin(360*(4/pd))*Ref(pr,-4))+
(Sin(360*(5/pd))*Ref(pr,-5))+
If(pd>6, Sin(360*(6/pd))*Ref(pr,-6), 0)+
If(pd>7, Sin(360*(7/pd))*Ref(pr,-7), 0)+
If(pd>8, Sin(360*(8/pd))*Ref(pr,-8), 0)+
If(pd>9, Sin(360*(9/pd))*Ref(pr,-9), 0)+
If(pd>10, Sin(360*(10/pd))*Ref(pr,-10), 0)+
If(pd>11, Sin(360*(11/pd))*Ref(pr,-11), 0)+
If(pd>12, Sin(360*(12/pd))*Ref(pr,-12), 0)+
If(pd>13, Sin(360*(13/pd))*Ref(pr,-13), 0)+
If(pd>14, Sin(360*(14/pd))*Ref(pr,-14), 0)

H rp sum 2
pd:=Int(Fml("Hilbert cycle period - final-a"));
pr:=(H+L)/2;
If(pd>15, Sin(360*(15/pd))*Ref(pr,-15), 0)+
If(pd>16, Sin(360*(16/pd))*Ref(pr,-16), 0)+
If(pd>17, Sin(360*(17/pd))*Ref(pr,-17), 0)+
If(pd>18, Sin(360*(18/pd))*Ref(pr,-18), 0)+
If(pd>19, Sin(360*(19/pd))*Ref(pr,-19), 0)+
If(pd>20, Sin(360*(20/pd))*Ref(pr,-20), 0)+
If(pd>21, Sin(360*(21/pd))*Ref(pr,-21), 0)+
If(pd>22, Sin(360*(22/pd))*Ref(pr,-22), 0)+
If(pd>23, Sin(360*(23/pd))*Ref(pr,-23), 0)+
If(pd>24, Sin(360*(24/pd))*Ref(pr,-24), 0)

H rp sum 3
pd:=Int(Fml("Hilbert cycle period - final-a"));
pr:=(H+L)/2;
If(pd>25, Sin(360*(25/pd))*Ref(pr,-25), 0)+
If(pd>26, Sin(360*(26/pd))*Ref(pr,-26), 0)+
If(pd>27, Sin(360*(27/pd))*Ref(pr,-27), 0)+
If(pd>28, Sin(360*(28/pd))*Ref(pr,-28), 0)+
If(pd>29, Sin(360*(29/pd))*Ref(pr,-29), 0)+
If(pd>30, Sin(360*(30/pd))*Ref(pr,-30), 0)+
If(pd>31, Sin(360*(31/pd))*Ref(pr,-31), 0)+
If(pd>32, Sin(360*(32/pd))*Ref(pr,-32), 0)+
If(pd>33, Sin(360*(33/pd))*Ref(pr,-33), 0)+
If(pd>34, Sin(360*(34/pd))*Ref(pr,-34), 0)

H TL sum 1
value:=Int(Fml("Hilbert cycle period - final-a"));
If(value=6, Mov((H+L)/2,8,S),0) +
If(value=7, Mov((H+L)/2,9,S),0) +
If(value=8, Mov((H+L)/2,10,S),0) +
If(value=9, Mov((H+L)/2,11,S),0) +
If(value=10, Mov((H+L)/2,12,S),0) +
If(value=11, Mov((H+L)/2,13,S),0) +
If(value=12, Mov((H+L)/2,14,S),0) +
If(value=13, Mov((H+L)/2,15,S),0) +
If(value=14, Mov((H+L)/2,16,S),0) +
If(value=15, Mov((H+L)/2,17,S),0)

H TL sum 2
value:=Int(Fml("Hilbert cycle period - final-a"));
If(value=16, Mov((H+L)/2,18,S),0) +
If(value=17, Mov((H+L)/2,19,S),0) +
If(value=18, Mov((H+L)/2,20,S),0) +
If(value=19, Mov((H+L)/2,21,S),0) +
If(value=20, Mov((H+L)/2,22,S),0) +
If(value=21, Mov((H+L)/2,23,S),0) +
If(value=22, Mov((H+L)/2,24,S),0) +
If(value=23, Mov((H+L)/2,25,S),0) +
If(value=24, Mov((H+L)/2,26,S),0) +
If(value=25, Mov((H+L)/2,27,S),0)

H TL sum 3
value:=Int(Fml("Hilbert cycle period - final-a"));
If(value=26, Mov((H+L)/2,28,S),0) +
If(value=27, Mov((H+L)/2,29,S),0) +
If(value=28, Mov((H+L)/2,30,S),0) +
If(value=29, Mov((H+L)/2,31,S),0) +
If(value=30, Mov((H+L)/2,32,S),0) +
If(value=31, Mov((H+L)/2,33,S),0) +
If(value=32, Mov((H+L)/2,34,S),0) +
If(value=33, Mov((H+L)/2,35,S),0) +
If(value=34, Mov((H+L)/2,36,S),0) +
If(value=35, Mov((H+L)/2,37,S),0)

Hilbert cycle period - 1a
value1:=((H+L)/2) - Ref(((H+L)/2),-6);
value2:= Ref(value1,-3);
value3:=0.75*(value1-Ref(value1,-6)) + 0.25*(Ref(value1,-2)-Ref(value1,-4));
inphase:= 0.33 * value2 + (0.67 * PREV);
quad:= 0.2 * value3 + ( 0.8 * PREV);
p1:=Atan(Abs(quad+Ref(quad,-1)),Abs(inphase+Ref(inphase,-1)));
phase:=If(inphase<0 AND quad>0, 180-p1,
If(inphase<0 AND quad<0, 180+p1,
If(inphase>0 AND quad<0, 360-p1,p1)));
dp:=If(Ref(phase,-1)<90 AND phase>270, 360+Ref(phase,-1)-phase,Ref(phase,-1)-phase);
dp2:=If(dp < 1, 1,
If(dp > 60, 60, dp));
dp2

Hilbert cycle period - final-a
c1:=Fml( "H cycle count 1a") + Fml( "H cycle count 2a") + Fml( "H cycle count 3a") ;
c2:=If(c1=0,PREV,c1);
(0.25*c2) + (0.75*PREV)

Instantaneous Trend Line
pr:=(H+L)/2;
(Fml("H TL sum 1") + Fml("H TL sum 2") + Fml("H TL sum 3"));
0.33*(pr + (0.5*(pr-Ref(pr,-3)))) + (0.67*PREV)

Sinewave Indicator
pd:=Int(Fml("Hilbert cycle period - final-a"));
cp:=Fml("Hilbert cycle period - final-a");
ip:=Fml( "H ip sum 1") + Fml( "H ip sum 2") + Fml( "H ip sum 3");
rp:=Fml( "H rp sum 1") + Fml( "H rp sum 2") + Fml( "H rp sum 3");
dc1:=If(Abs(ip)>0.001, Atan(rp/ip,1), 90*If(rp>=0,1,-1));
dc2:=If(pd<30 AND cp>0,dc1+((6.818/cp - 0.227)*360),dc1);
dc3:=If(ip<0, dc2+270, dc2+90);
dcp:=If(dc3>315, dc3-360, dc3);
Sin(dcp);
Sin(dcp+45)

Code:

Here is the code for use in MetaStock 6.52 orhigher for the instantaneous trendline and sinewave indicator as described by John Ehlers in "Adaptive Trends And Oscillators" in thisissue. To implement them, the following formulas must be created in MetaStock's Indicator Builder.

Each formula must be created separately and must be named exactly as it appears below. Only the last two formulas are plotted, so you may wish to prevent the others from being displayed in the Indicator QuickList by unchecking the "Display In QuickList" option when creating the formula.

These formulas can also be downloaded from:
http://www.equis.com/customer/support/formulas/

Author: John Ehlers
Source: http://www.equis.com

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