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APPENDIX I [the mathematical proof of the
basic tClose relation]
The main principle of this predictions series is the
<FONT
size=2>tClose=(p*(k-1)*MA(C,k-1)-k*(p-1)*MA(C,p-1))/(k-p);
for tomorrows Close necessary for an MAk, MAp
touch.For those interested, here is the mathematical proof:
LetMAk=MA(C,k)and MAp=MA(C,p)For tomorrow, the
respective values for C, MAk and MAp will be calledtC, tMAk and
tMApApplying the definition of moving average for tMAk and tMAp, we shall
havetMAk=(tC+C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2))/ktMAp=(tC+C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2))/pIf
tMAk=tMAp,
then(tC+C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2))/k=(tC+C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2))/p,
orp*(tC+C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2))=k*(tC+C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2)),
orp*tC+p*(C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2))=k*tC+k*(C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2))Let
k>p.
Thenp*(C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2))-k*(C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2))=(k-p)*tC
[relation R0]SinceMA(k-1)=(C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2))/(k-1)
[relationA0]and MA(p-1)=(C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2))/(p-1)
[relation B0]or(k-1)*MA(k-1)=C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(k-2)
[relationA1]and(p-1)*MA(p-1)=C+Ref(C,-1)+Ref(C,-2)+...+Ref(C,-(p-2)
[relation B1]Substituting relA1 and relB1 into relR0 we
havep*(k-1)*MA(k-1)-k*(p-1)*MA(p-1)=(k-p)*tC or, in AFL
termsp*(k-1)*MA(C,k-1)-k*MA(C,p-1)=(k-p)*tC or, finally
tC=(p*(k-1)*MA(C,k-1)-k*MA(C,p-1))/(k-p), for
k>p
Dimitris Tsokakis
PART II : PREDICTIONS
FOR THE CROSS OF TWO INDICATOR MOVING AVERAGES
The same principle may be used to predict a cross of two MAs
of an indicator.
Example : The StochD() indicator and its MAk=MA(StochD(),k)
and MAp=MA(StochD(),p).
We just need to replace C by StochD() in the original
Prediction formula.
The results are impressive, false predictions are
rare.
The majority of Accurate predictions are confirmed the very
next bar, the Acc2Desc and Acc2Asc,
ie predictions verified two bars later is totally<FONT
size=2> removed from the N100 study and, actually, are included
here just for the comparison [both columns are zero for ALL
N100 stocks, for the last 43 months...]
After this extended test, we may say that the cross of two
StochD() MAs is successfully predicted.
Use the following exploration [n=1 last quotations] for the
absolute # of crosses
// Prediction of MAcross of
StochD()C1=StochD();p=20;MAp=MA(C1,p);k=30;MAk=MA(C1,k);y=p*MA(C1,p)-(p-1)*Ref(MA(C1,p-1),-1);tC1=(p*(k-1)*MA(C1,k-1)-k*(p-1)*MA(C1,p-1))/(k-p);DescCrossPrediction=Cross(tC1,C1);AscCrossPrediction=Cross(C1,tC1);ConfirmedDesc=Cross(MAk,MAp);ConfirmedAsc=Cross(MAp,MAk);DescTotalPredictions=Cum(DescCrossPrediction);Accurate0DescPredictions=Cum(ConfirmedDesc
AND Ref(DescCrossPrediction,-1));Accurate1DescPredictions=Cum(ConfirmedDesc
AND Ref(DescCrossPrediction,-2));Accurate2DescPredictions=Cum(ConfirmedDesc
AND Ref(DescCrossPrediction,-3));UselessDescPredictions=Cum(ConfirmedDesc
AND
DescCrossPrediction);AscTotalPredictions=Cum(AscCrossPrediction);Accurate0AscPredictions=Cum(ConfirmedAsc
AND Ref(AscCrossPrediction,-1));Accurate1AscPredictions=Cum(ConfirmedAsc AND
Ref(AscCrossPrediction,-2));Accurate2AscPredictions=Cum(ConfirmedAsc AND
Ref(AscCrossPrediction,-3));UselessAscPredictions=Cum(ConfirmedAsc AND
AscCrossPrediction);Filter=1;AddColumn(Accurate0DescPredictions,"Acc0
Desc",1.0);AddColumn(Accurate1DescPredictions,"Acc1
Desc",1.0);AddColumn(Accurate2DescPredictions,"Acc2
Desc",1.0);AddColumn(UselessDescPredictions,"Useless
Desc",1.0);AddColumn(DescTotalPredictions-Column0-Column1-Column2-Column3,"False
Desc",1.0);AddColumn(Accurate0AscPredictions,"Acc0
Asc",1.0);AddColumn(Accurate1AscPredictions,"Acc1
Asc",1.0);AddColumn(Accurate2AscPredictions,"Acc2
Asc",1.0);AddColumn(UselessAscPredictions,"Useless
Asc",1.0);AddColumn(AscTotalPredictions-Column5-Column6-Column7-Column8,"False
Asc",1.0);
[see some results in the upper gif]
and the following exploration for the %
success
// % Prediction of MAcross of
StochD()C1=StochD();p=20;MAp=MA(C1,p);k=30;MAk=MA(C1,k);y=p*MA(C1,p)-(p-1)*Ref(MA(C1,p-1),-1);tC1=(p*(k-1)*MA(C1,k-1)-k*(p-1)*MA(C1,p-1))/(k-p);DescCrossPrediction=Cross(tC1,C1);AscCrossPrediction=Cross(C1,tC1);ConfirmedDesc=Cross(MAk,MAp);ConfirmedAsc=Cross(MAp,MAk);DescTotalPredictions=Cum(DescCrossPrediction);Accurate0DescPredictions=Cum(ConfirmedDesc
AND Ref(DescCrossPrediction,-1));Accurate1DescPredictions=Cum(ConfirmedDesc
AND Ref(DescCrossPrediction,-2));Accurate2DescPredictions=Cum(ConfirmedDesc
AND Ref(DescCrossPrediction,-3));UselessDescPredictions=Cum(ConfirmedDesc
AND
DescCrossPrediction);AscTotalPredictions=Cum(AscCrossPrediction);Accurate0AscPredictions=Cum(ConfirmedAsc
AND Ref(AscCrossPrediction,-1));Accurate1AscPredictions=Cum(ConfirmedAsc AND
Ref(AscCrossPrediction,-2));Accurate2AscPredictions=Cum(ConfirmedAsc AND
Ref(AscCrossPrediction,-3));UselessAscPredictions=Cum(ConfirmedAsc AND
AscCrossPrediction);Filter=1;AddColumn(100*Accurate0DescPredictions/DescTotalPredictions,"Acc0
Desc
%",1.0);AddColumn(100*Accurate1DescPredictions/DescTotalPredictions,"Acc1
Desc
%",1.0);AddColumn(100*Accurate2DescPredictions/DescTotalPredictions,"Acc2
Desc
%",1.0);AddColumn(100*UselessDescPredictions/DescTotalPredictions,"Useless
Desc %",1.0);AddColumn(100-Column0-Column1-Column2-Column3,"False Desc
%",1.0);AddColumn(100*Accurate0AscPredictions/AscTotalPredictions,"Acc0 Asc
%",1.0);AddColumn(100*Accurate1AscPredictions/AscTotalPredictions,"Acc1 Asc
%",1.0);AddColumn(100*Accurate2AscPredictions/AscTotalPredictions,"Acc2 Asc
%",1.0);AddColumn(100*UselessAscPredictions/AscTotalPredictions,"Useless Asc
%",1.0);AddColumn(100-Column5-Column6-Column7-Column8,"False Asc
%",1.0);
[the respective results in the lower gif]
Dimitris Tsokakis
PART I : PREDICTIONS FOR THE CROSS OF
TWO MOVING AVERAGES
To make the probable cross window more narrow, let
us forget the unexpected +50% or -50% daily return.
Each stock has a history, including gapups and
gapdowns.
The new hypothesis is that the stock will not
double its historical highest ROC(C,1).
For the Upper [Lower] limit we have
<DIV
>UR=2*Highest(ROC(C,1));LR=2*Lowest(ROC(C,1));
and the respective coefficients will
beUcoeff=1+UR/100;Lcoeff=1+LR/100;
and the more realistic condition will
beFilter=tClose<Lcoeff*C OR tClose>Ucoeff*C;
You will see now very few bars to expect an
MAcross [the black candles in the att. gif]
The updated Title helps for info through the
interpretation window.[it is also an extended use of Boolean operators]
// Probable MAcross
bars
<FONT
face="Times New Roman">p=20;MAp=MA(C,p);k=30;MAk=MA(C,k);y=p*MA(C,p)-(p-1)*Ref(MA(C,p-1),-1);tClose=(p*(k-1)*MA(C,k-1)-k*(p-1)*MA(C,p-1))/(k-p);DescCrossPrediction=Cross(tClose,C);AscCrossPrediction=Cross(C,tClose);ExpectMAcross=DescCrossPrediction
OR AscCrossPrediction;Confirmed=Cross(MAk,MAp) OR
Cross(MAp,MAk);UR=2*Highest(ROC(C,1));LR=2*Lowest(ROC(C,1));Ucoeff=1+UR/100;Lcoeff=1+LR/100;Filter=tClose<Lcoeff*C
OR
tClose>Ucoeff*C;AddColumn(MAp,"MAp");AddColumn(MAk,"MAk");Plot(C,"",7*Filter+1,64);Plot(MAp,"",4,1);Plot(MAk,"",5,1);bars=BarsSince(Cross(MAp,MAk)
OR Cross(MAk,MAp));expect=NOT(Filter);Title=Name()+" ,
"+WriteIf(expect AND NOT(expectMAcross) AND NOT(Confirmed) AND bars>3 AND
tClose<C,"EXPECT a bearish MAcross SOON","")+WriteIf(expect AND
NOT(expectMAcross) AND NOT(Confirmed) AND bars>3 AND tClose>C,"EXPECT a
bullish MAcross SOON","")+WriteIf(DescCrossPrediction,"EXPECT a bearish
MAcross TOMORROW","")+WriteIf(AscCrossPrediction,"EXPECT a bullish MAcross
TOMORROW","")+WriteIf(Confirmed,"MAcross","");In many cases now, there
is one "EXPECT SOON" and one "EXPECT TOMORROW".
Dimitris
Tsokakis
---- Original Message -----
<DIV
>From: <A
href="" title=tsokakis@xxxxxxxxx>Dimitris Tsokakis
To: <A
href=""
title=amibroker@xxxxxxxxxxxxxxx>amibroker@xxxxxxxxxxxxxxx
Sent: Thursday, July 17, 2003 2:35 PM
Subject: Fw: Predictions I
Let us see now the more realististic
approach:
Hypothesis : We do not expect for
tomorrow a daily return greater than +50% OR less than -50%
.
Then you will find out very few days to expect the
MAcrossover.
Some times we see two or three premature signals before the
main one.
This observation helps to speculate in advance the upcoming
MAcross and find best intraday prices for your movement.
We may have 3 types of signals
*EXPECT an MAcross SOON
*EXPECT an MAcross TOMORROW
*an MAcross confirmation
to check the value of the method.
Use for your ind. builder [interpretation window] the
code
// MA cross
Expectationp=20;MAp=MA(C,p);k=30;MAk=MA(C,k);y=p*MA(C,p)-(p-1)*Ref(MA(C,p-1),-1);tClose=(p*(k-1)*MA(C,k-1)-k*(p-1)*MA(C,p-1))/(k-p);DescCrossPrediction=Cross(tClose,C);AscCrossPrediction=Cross(C,tClose);ExpectMAcross=DescCrossPrediction
OR AscCrossPrediction;Filter=tClose<0.5*C OR
tClose>1.5*C;AddColumn(MAp,"MAp");AddColumn(MAk,"MAk");Plot(C,"",7*Filter+1,64);Plot(MAp,"",4,1);Plot(MAk,"",5,1);bars=BarsSince(Cross(MAp,MAk)
OR Cross(MAk,MAp));expect=NOT(Filter) AND
NOT(ExpectMAcross);Title=Name()+" , "+WriteIf(expect AND bars>=2,"EXPECT
an MAcross SOON","")+WriteIf(ExpectMAcross,"EXPECT an MAcross
TOMORROW","");
to read the respective signals.
In the att. gif, all the olive candles are far from any
probable MAcross, the big black candle gives
the premature expectation signal and the very next bar
predicts [successfully] that an MAcross will occur tomorrow.
Dimitris Tsokakis
----- Original Message -----
From: <A
href="" title=tsokakis@xxxxxxxxx>Dimitris Tsokakis
To: <A href=""
title=amibroker@xxxxxxxxxxxxxxx>amibroker@xxxxxxxxxxxxxxx
Sent: Thursday, July 17, 2003 11:17 AM
Subject: Fw: Predictions I
The conditions DescCrossPrediction or
AscCrossPrediction give a quite reliable warning for an upcoming MA cross,
bullish or bearish.
There are some periods when this cross is IMPOSSIBLE and may
be accurately idendified.
This tClose is the virtual next bar Close which will fulfill
the condition MA(C,p)=MA(C;k).
The argument is quite simple:
If tClose is negative, then it is IMPOSSIBLE
to see an MAcross tomorrow.
[Of course there are many other cases we may exclude, for
example tClose=0.1*C, since we do not expect a -90% daily return for CSCO
!!!
but, in this formula we just want to investigate the
theoretical IMPOSSIBLE]
For your indicator builder [or AA] use the
// Impossible MA cross Prediction
p=20;MAp=MA(C,p);k=30;MAk=MA(C,k);y=p*MA(C,p)-(p-1)*Ref(MA(C,p-1),-1);tClose=(p*(k-1)*MA(C,k-1)-k*(p-1)*MA(C,p-1))/(k-p);Filter=tClose<0;AddColumn(MAp,"MAp");AddColumn(MAk,"MAk");Plot(C,"",6*Filter+1,64);Plot(MAp,"",4,1);Plot(MAk,"",5,1);
In AA explore the database for the n=1 last quotations to see
all these stocks you do not expect an MA cross, bullish or bearish.
Any MAcross technique should be applied to the
rest...
For July16 there were 18 N100 stocks indifferent for an
MAcross.
Dimitris Tsokakis
----- Original Message -----
From: <A
href="" title=tsokakis@xxxxxxxxx>Dimitris Tsokakis
To: <A href=""
title=amibroker@xxxxxxxxxxxxxxx>amibroker@xxxxxxxxxxxxxxx
Sent: Wednesday, July 16, 2003 11:04 AM
Subject: Fw: Predictions I
The condition
DescCrossPrediction=Cross(tClose,C);
predicts that a Descending MA cross will occur
tomorrow.
It will be named
<FONT
face="Times New Roman">
Accurate0DescPredictions, if it is confirmed tomorrow<FONT
face=Verdana size=2>
Accurate1DescPredictions, if it is confirmed 1 day later<FONT
face=Verdana size=2>
Accurate2DescPredictions, if it is confirmed 2 days
later
UselessDescPredictions, if it is simultaneous
with the prediction
False, if it does not belong in one above
category.
[Last bar predictions are also considered as
false, although the majority will be confirmed tomorrow...]
Similar terminology is used for the Ascending
crosses.
The N100 results from Jan2000 till now are
enthusiastic and, in practical terms, we may say that we can have a safe
prediction
for the [unknown] next bar MA
cross.
Explore your database for the n=1 last
quotations with
// MA cross Prediction Statistics, by Dimitris
Tsokakis, July 2003 <FONT
face="Times New Roman">
p=20;MAp=<FONT
size=2>MA(C,p);<FONT face=Verdana
size=2>
k=30;MAk=<FONT
size=2>MA(C,k);<FONT face=Verdana
size=2>
y=p*MA(C,p)-(p-<FONT
size=2>1)*Ref<FONT
size=2>(MA(C,p-<FONT
size=2>1),-1<FONT
size=2>);<FONT face=Verdana
size=2>
tClose=(p*(k-1)*<FONT
size=2>MA(C,k-1<FONT
size=2>)-k*(p-1)*<FONT
size=2>MA(C,p-1<FONT face=Verdana
size=2>))/(k-p);<FONT
face="Times New Roman">
DescCrossPrediction=Cross<FONT
face=Verdana size=2>(tClose,C);<FONT
face="Times New Roman">
AscCrossPrediction=Cross<FONT
face=Verdana size=2>(C,tClose);<FONT
face="Times New Roman">
ConfirmedDesc=Cross<FONT face=Verdana
size=2>(MAk,MAp);<FONT
face="Times New Roman">
ConfirmedAsc=Cross<FONT face=Verdana
size=2>(MAp,MAk);<FONT
face="Times New Roman">
DescTotalPredictions=Cum<FONT
face=Verdana size=2><FONT
face="Times New Roman">(DescCrossPrediction);<FONT
face="Times New Roman">
Accurate0DescPredictions=Cum<FONT
size=2>(ConfirmedDesc AND Ref<FONT
size=2>(DescCrossPrediction,-1<FONT face=Verdana
size=2>));<FONT
face="Times New Roman">
Accurate1DescPredictions=Cum<FONT
size=2>(ConfirmedDesc AND Ref<FONT
size=2>(DescCrossPrediction,-2<FONT face=Verdana
size=2>));<FONT
face="Times New Roman">
Accurate2DescPredictions=Cum<FONT
size=2>(ConfirmedDesc AND Ref<FONT
size=2>(DescCrossPrediction,-3<FONT face=Verdana
size=2>));<FONT
face="Times New Roman">
UselessDescPredictions=Cum<FONT
face=Verdana size=2>(ConfirmedDesc AND
DescCrossPrediction);
AscTotalPredictions=Cum<FONT face=Verdana
size=2>(AscCrossPrediction);<FONT
face="Times New Roman">
Accurate0AscPredictions=Cum<FONT
size=2>(ConfirmedAsc AND Ref<FONT
size=2>(AscCrossPrediction,-1<FONT face=Verdana
size=2>));<FONT
face="Times New Roman">
Accurate1AscPredictions=Cum<FONT
size=2>(ConfirmedAsc AND Ref<FONT
size=2>(AscCrossPrediction,-2<FONT face=Verdana
size=2>));<FONT
face="Times New Roman">
Accurate2AscPredictions=Cum<FONT
size=2>(ConfirmedAsc AND Ref<FONT
size=2>(AscCrossPrediction,-3<FONT face=Verdana
size=2>));<FONT
face="Times New Roman">
UselessAscPredictions=Cum<FONT
face=Verdana size=2>(ConfirmedAsc AND
AscCrossPrediction);
Filter=1<FONT
face="Times New Roman">;<FONT
face="Times New Roman">
AddColumn(100<FONT
size=2>*Accurate0DescPredictions/DescTotalPredictions,"Acc0
Desc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*Accurate1DescPredictions/DescTotalPredictions,"Acc1
Desc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*Accurate2DescPredictions/DescTotalPredictions,"Acc2
Desc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*UselessDescPredictions/DescTotalPredictions,"Useless
Desc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>-Column0-Column1-Column2-Column3,"False Desc
%",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*Accurate0AscPredictions/AscTotalPredictions,"Acc0
Asc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*Accurate1AscPredictions/AscTotalPredictions,"Acc1
Asc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*Accurate2AscPredictions/AscTotalPredictions,"Acc2
Asc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>*UselessAscPredictions/AscTotalPredictions,"Useless
Asc %",1.0<FONT face=Verdana
size=2>);<FONT
face=Verdana size=2>
AddColumn(100<FONT
size=2>-Column5-Column6-Column7-Column8,"False Asc
%",1.0<FONT face=Verdana
size=2>);
----- Original Message -----
From: <A
href="" title=tsokakis@xxxxxxxxx>Dimitris Tsokakis
To: <A href=""
title=amibroker@xxxxxxxxxxxxxxx>amibroker@xxxxxxxxxxxxxxx
Sent: Tuesday, July 15, 2003 5:35 PM
Subject: Predictions I
We may calculate the next bar Close necessary for a MA(C,p) to
cross another MA(C,k).
I will overcome this procedure and I will try just to predict
if a cross will occur tomorrow.
For your AA window explore for the n=1 last quotations
with
// Prediction for a cross of two moving averages
<FONT
size=2>p=20;MAp=MA(C,p);Plot(MAp,"",1,8);k=30;MAk=MA(C,k);Plot(MAk,"",2,8);y=p*MA(C,p)-(p-1)*Ref(MA(C,p-1),-1);//Plot(Ref(C,0),"",7,8);tClose=(p*(k-1)*MA(C,k-1)-k*(p-1)*MA(C,p-1))/(k-p);DescCrossPrediction=Cross(tClose,C);AscCrossPrediction=Cross(C,tClose);ConfirmedDesc=Cross(MAk,MAp);ConfirmedAsc=Cross(MAp,MAk);Title=Name()+WriteIf(ConfirmedDesc,",
Confirmed descending MAcross","")+WriteIf(DescCrossPrediction,", A
descending MAcross will occur tomorrow","")+WriteIf(ConfirmedAsc,",
Confirmed ascending MAcross","")+WriteIf(AscCrossPrediction,", An ascending
MAcross will occur
tomorrow","");Filter=1;AddColumn(Cum(DescCrossPrediction),"Predicted
DescCrosses",1.0);AddColumn(Cum(ConfirmedDesc),"Confirmed
DescCrosses",1.0);AddColumn(100*Cum(DescCrossPrediction)/Cum(ConfirmedDesc),"Desc
%");AddColumn(Cum(AscCrossPrediction),"Predicted
AscCrosses",1.0);AddColumn(Cum(ConfirmedAsc),"Confirmed
AscCrosses",1.0);AddColumn(100*Cum(AscCrossPrediction)/Cum(ConfirmedAsc),"Asc
%",1.0);
to see the commulative predicted/actual cross
relation.
Replace the Filter=1; line with the
Filter=<FONT
color=#000000 face="Times New Roman">AscCrossPrediction OR
DescCrossPrediction;
<FONT color=#000000
face="Times New Roman">to see the predictions for tomorrow, or with the
<FONT color=#000000
face="Times New Roman">Filter=<FONT color=#ffffe0
face=Verdana><FONT color=#000000 face="Times New Roman"
size=2>Ref(AscCrossPrediction OR DescCrossPrediction,-1);<FONT
size=2>
to see the confirmed
crosses
The commulative view for my favorites selection is in the
attached gif.
A detailed analysis will follow.
Use the same formula in Indicator Builder or Interpretation
window.
Dimitris Tsokakis
[to be continued]
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