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Adaptive Trends And Oscillators by John Ehlers
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/

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)

 

e-w-Adaptive_Trends_And_Oscillators.gif
 
-- Cheryl Elton, Equis International
Source / From: TOP
http://www.equis.com

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