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[amibroker] The dmi MA, EMA cross and the Prediction theory



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Yuli, Jason,
in your dmi example, the Buy, Sell conditions 
were
 
Buy=Cross(<FONT 
size=2>EMA(dmi,pds),<FONT 
size=2>MA<FONT 
face="Times New Roman">(dmi,pds1));
Sell=Cross(<FONT 
size=2>MA(dmi,pds1),EMA<FONT 
face=Verdana size=2>(dmi,pds));
 
It is a special case 
of an EMA, MA cross.
The mathematical 
condition for an EMAp, MAk touch is
 <FONT 
face="Times New Roman">
tdmi=((p+1)*<FONT 
size=2>MA<FONT 
size=2>(dmi,k-1)*(k-<FONT 
size=2>1)-k*(p-1<FONT 
size=2>)*EMAp)/(2*k-(p+<FONT 
size=2>1));
 
where tdmi is the tomorrow dmi 
value.
According to the similar predictions 
arguments, the crosses of this tdmi with dmi itself should
anticipate by one bar the actual EMA, 
MA crosses.
You may verify this from the 
code
 
//Dynamic Momentum Index Tushar Chande 
Translated to AFL by Jayson Casavant//Cmo5 
formula<FONT 
face="Times New Roman">
CMO5_1=Sum<FONT 
face="Times New Roman">( IIf<FONT 
face="Times New Roman">( C > <FONT 
size=2>Ref( C, 
-1 ) , ( C - <FONT 
size=2>Ref( C 
,-1 ) ) ,<FONT 
size=2>0 ) ,5<FONT 
face=Verdana size=2> ) ;<FONT 
face="Times New Roman">
CMO5_2=Sum<FONT 
face="Times New Roman">( IIf<FONT 
face="Times New Roman">( C < <FONT 
size=2>Ref( C 
,-1 ) , ( <FONT 
size=2>Ref( C 
,-1 ) - C ) ,<FONT 
size=2>0 ) ,5<FONT 
face=Verdana size=2> );<FONT 
face="Times New Roman">
CMO5=DEMA<FONT 
face="Times New Roman">(100 
* (( CMO5_1 -CMO5_2) /( CMO5_1+CMO5_2)),3<FONT 
face=Verdana size=2>);<FONT 
face=Verdana size=2>//Cmo10 
formula<FONT 
face="Times New Roman">
CMO10_1=Sum<FONT 
face="Times New Roman">( IIf<FONT 
face="Times New Roman">( C > <FONT 
size=2>Ref( C, 
-1 ) , ( C - <FONT 
size=2>Ref( C 
,-1 ) ) ,<FONT 
size=2>0 ) ,10<FONT 
face=Verdana size=2> ) ;<FONT 
face="Times New Roman">
CMO10_2=Sum<FONT 
face="Times New Roman">( IIf<FONT 
face="Times New Roman">( C < <FONT 
size=2>Ref( C 
,-1 ) , ( <FONT 
size=2>Ref( C 
,-1 ) - C ) ,<FONT 
size=2>0 ) ,10<FONT 
face=Verdana size=2> );<FONT 
face="Times New Roman">
CMO10=DEMA<FONT 
face="Times New Roman">(100 
* (( CMO10_1 -CMO10_2) /( CMO10_1+CMO10_2)),<FONT 
size=2>3<FONT 
face="Times New Roman">);<FONT 
face="Times New Roman">//Cmo20 formula<FONT face=Verdana 
size=2>
CMO20_1=Sum<FONT 
face="Times New Roman">( IIf<FONT 
face="Times New Roman">( C > <FONT 
size=2>Ref( C, 
-1 ) , ( C - <FONT 
size=2>Ref( C 
,-1 ) ) ,<FONT 
size=2>0 ) ,20<FONT 
face=Verdana size=2> ) ;<FONT 
face="Times New Roman">
CMO20_2=Sum<FONT 
face="Times New Roman">( IIf<FONT 
face="Times New Roman">( C < <FONT 
size=2>Ref( C 
,-1 ) , ( <FONT 
size=2>Ref( C 
,-1 ) - C ) ,<FONT 
size=2>0 ) ,20<FONT 
face=Verdana size=2> );<FONT 
face="Times New Roman">
CMO20=DEMA<FONT 
face="Times New Roman">(100 
* (( CMO20_1 -CMO20_2) /( CMO20_1+CMO20_2)),<FONT 
size=2>3<FONT 
face="Times New Roman">);<FONT 
face="Times New Roman">// dmi formula<FONT face=Verdana 
size=2>
dmi=((StDev<FONT 
face="Times New Roman">(C,5<FONT 
size=2>)* CMO5)+(StDev<FONT 
face="Times New Roman">(C,10<FONT 
size=2>)* CMO10)+(StDev<FONT 
face="Times New Roman">(C,20<FONT 
face=Verdana size=2>)*<FONT 
face="Times New Roman">
CMO20))/(StDev<FONT 
face="Times New Roman">(C,5<FONT 
size=2>)+StDev<FONT 
face="Times New Roman">(C,10<FONT 
size=2>)+StDev<FONT 
face="Times New Roman">(C,20<FONT 
face=Verdana size=2>));<FONT 
face="Times New Roman">
pds=Optimize<FONT 
face="Times New Roman">("Smoothing"<FONT 
size=2>,10,<FONT 
size=2>1,10<FONT 
size=2>,1<FONT 
face="Times New Roman">);
pds1=Optimize<FONT 
face="Times New Roman">("Trigger 
Line",4,<FONT 
size=2>1,10<FONT 
size=2>,1<FONT 
face="Times New Roman">);
Buy=Cross(<FONT 
size=2>EMA(dmi,pds),<FONT 
size=2>MA<FONT 
face="Times New Roman">(dmi,pds1));
Sell=Cross<FONT 
face="Times New Roman">(MA<FONT 
face="Times New Roman">(dmi,pds1),<FONT 
size=2>EMA<FONT face="Times New Roman" 
size=2>(dmi,pds));
 
// Prediction of 
actual crosses by D. Tsokakis
p=pds;EMAp=EMA<FONT face=Verdana 
size=2>(dmi,p);<FONT 
face="Times New Roman">
k=pds1;MAk=MA<FONT face=Verdana 
size=2>(dmi,k);<FONT 
face="Times New Roman">
tdmi=((p+1)*<FONT 
size=2>MA<FONT 
size=2>(dmi,k-1)*(k-<FONT 
size=2>1)-k*(p-1<FONT 
size=2>)*EMAp)/(2*k-(p+<FONT 
size=2>1<FONT 
face="Times New Roman">));
Buy1=Cross<FONT 
face="Times New Roman">(t,dmi);Sell1=<FONT 
size=2>Cross<FONT 
face="Times New Roman">(dmi,t);<FONT face=Verdana 
size=2>
Plot(Buy,""<FONT 
size=2>,5,<FONT 
size=2>2);Plot<FONT 
size=2>(Sell,"",<FONT 
size=2>4,2<FONT 
face=Verdana size=2>);<FONT 
face=Verdana size=2>
Plot(Buy1,""<FONT 
size=2>,1,<FONT 
size=2>1);Plot<FONT 
size=2>(Sell1,"",<FONT 
size=2>2,1<FONT face=Verdana 
size=2>);
 
The red [Sell], 
green [Buy] bars are the actual crosses, the white, black smaller bars are the 
respective predictions.
You may see the 
prediction success, although let me doubt about the probable 
use.
The system gave me 
some worse backtesting results, when I tried delay=0 [instead of the regular 
delay=1]
and gave also worse 
results when I tried Buy1/Sell1 instead of Buy/Sell.
Anyway, I hope it 
will be useful for your study.
Dimitris 
Tsokakis
 
 
 






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