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Thank you DT,
The problem is different. We need to know the value of tomorrow's Ct when
two OTHER arrays cross, NOT when the Ct crosses anything: Ct is not required
to touch any line. I do not know how to explain it better: the objective is
to know at what value of Ct the other two functions cross, i.e. find Ct when
a F1(Ct) touches F2(Ref(Array,-1)). This is probably a more useful
application than having the raw C touch any line because the C is subject to
a lot of noise and would give many false signals.  I think your innovative
math functions provide the solution for this problem but i can't figure out
how, I hoped my code would illustrated the problem more clearly... Forgive
me if i am just plain dumb and the solution is staring at me.
Anyway, thanks very much for your time DT,
best regards,
herman.
  -----Original Message-----
  From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@xxxxxxxxx]
  Sent: Tuesday, October 26, 2004 2:08 AM
  To: amibroker@xxxxxxxxxxxxxxx
  Subject: [amibroker] Re: DT's Ct prediction for the Ti3
  Herman,
  The formula is correct and gives the next bar close Ct as a function
  of tomorrow´s Ti3Ct.
  When Ti3Ct value is known [or equal to another function] then Ct is
  calculated.
  For a simple verification, set
  Ti3Ct=Ref(Ti3C,1);
  and then Ct will be EXACTLY the Ref(C,1).
  Plot(C,"C",colorBlack,1);
  periods=5;s=0.7;f=2/(periods+1);R=1-f;
  //the Ti3C
  price=C;
  e1C=EMA(price,periods);
  e2C=EMA(e1C,Periods);
  e3C=EMA(e2C,Periods);
  e4C=EMA(e3C,Periods);
  e5C=EMA(e4C,Periods);
  e6C=EMA(e5C,Periods);
  c1=-s*s*s;
  c2=3*s*s+3*s*s*s;
  c3=-6*s*s-3*s-3*s*s*s;
  c4=1+3*s+s*s*s+3*s*s;
  Ti3C=c1*e6C+c2*e5C+c3*e4C+c4*e3C;
  Ti3Ct=Ref(Ti3C,1);// condition
  //the Ct as a function of Ti3Ct
  Ct=(Ti3Ct-R*(c1*(f^5*e1C+f^4*e2C+f^3*e3C+f^2*e4C+f*e5C+e6C)+c2*
  (f^4*e1C+f^3*e2C+f^2*e3C+f*e4C+e5C)+c3*(f^3*e1C+f^2*e2C+f*e3C+e4C)+c4*
  (f^2*e1C+f*e2C+e3C)))/(C1*f^6+C2*f^5+C3*f^4+C4*f^3) ;
  Plot(Ref(Ct,-1),"Ct",colorRed,8);
  Dimitris
  --- In amibroker@xxxxxxxxxxxxxxx, "Herman van den Bergen"
  <psytek@xxxx> wrote:
  > Hello DT,
  >
  > I really appreciate your help with this however is that your
  solution looks
  > somewhat the same but isn't accurate...perhaps you misunderstood
  and are
  > calculating something else...
  >
  > The best way for me to illustrate my need is with a generic
  iterative
  > solution. Sorry to impose on you DT but to see how the result
  differs you
  > have to display both your solution and mine. When you have loaded
  the demo
  > code below, click on any bar and open the Param() window. Then
  apply an
  > offset to the selected close price until you see the two T3s (white
  and
  > black) cross, at that point the C price is exactly on the Predicted
  Close
  > price (Red). This is not the case with your formula. Note that I
  moved the
  > Red predicted value forward one bar to allow easier comparison to
  the Close
  > and show a little square when the target is hit. The key
  requirement of
  > course it that C falls exactly on the predicted value when the T3s
  cross -
  > this doesn't happen with your indicator.
  >
  > With EOD data and restricting the calculation to the display area
  only, my
  > solutions works OK, but i need a continuous indicator for the
  entire data RT
  > history, this means about 100K bars. If your formula worked it
  would enable
  > me to do that!!!
  >
  > Any change of making your solution match mine?
  >
  > thanks again DT,
  > herman.
  >
  >
  > --------------------------------------------------------------------
  --------
  > ----
  >
  > SetBarsRequired(1000000,1000000);
  >
  > function Ti3(array,p,s)
  >  {
  >  f=2/(p+1);
  >  e1=EMA(array,p);
  >  e2=EMA(e1,p);
  >  e3=EMA(e2,p);
  >  e4=EMA(e3,p);
  >  e5=EMA(e4,p);
  >  e6=EMA(e5,p);
  >  c1=-s*s*s;
  >  c2=3*s*s+3*s*s*s;
  >  c3=-6*s*s-3*s-3*s*s*s;
  >  c4=1+3*s+s*s*s+3*s*s;
  >  T3=c1*e6+c2*e5+c3*e4+c4*e3;
  >  return T3;
  >  }
  >
  > function ReferenceFunction( ReferenceArray )
  >  {
  >  global T3Periods, T3Sensitivity, ResetReference;
  >  R = Ti3( ReferenceArray, T3Periods ,T3Sensitivity);
  >  return R;
  >  }
  >
  > function TestFunction( TestArray )
  >  {
  >  global T3Periods, T3Sensitivity, ResetReference;
  >  R = Ti3( TestArray, T3Periods ,T3Sensitivity);
  >  return R;
  >  }
  >
  > function GetTriggerPrice( ReferenceArray, TestArray, TestBarNum,
  T3Period,
  > T3Sensitivity )
  >  {
  >  Precision  = 0.0001;
  >
  >  RefArray  = ReferenceFunction( ReferenceArray );
  >  RefValue  = RefArray[TestBarNum ];
  >
  >  TestValue = TestArray[TestBarNum];
  >  TestIncr  = TestValue/3;
  >
  >  do {
  >   TestArray[TestBarNum ]  = TestValue;
  >   T3t     = TestFunction( TestArray);
  >   TodaysT3   = T3t[TestBarNum ];
  >   if( abs(TodaysT3-RefValue) < Precision );
  >   else if(TodaysT3< RefValue) TestValue= TestValue+ TestIncr ;
  >   else TestValue= TestValue- TestIncr ;
  >   TestIncr = TestIncr /2;
  >   Error = abs(TodaysT3- RefValue);
  >   } while ( Error > Precision );
  >
  >  return TestArray[TestBarNum ];
  >  }
  >
  > PriceOffSet = Param("Price offset",0,-2,2,0.001);
  > BarNum = SelectedValue(BarIndex());
  > CursorBar = BarNum == BarIndex();
  > ParamPrice = C + PriceOffSet;
  > C = IIf(CursorBar, ParamPrice, C);
  > ReferenceArray = Ref(H,-1);
  > TestArray = C;
  > T3Periods = 3;
  > T3Sensitivity = 0.7;
  >
  > FirstVisibleBar = Status( "FirstVisibleBar");
  > Lastvisiblebar = Status("LastVisibleBar");
  > TP=Null;
  > for( b = Firstvisiblebar; b < Lastvisiblebar AND b < BarCount; b++)
  >  {
  >  TP[b] = GetTriggerPrice( ReferenceArray, TestArray, b, T3Periods,
  > T3Sensitivity );
  >  }
  >
  > TargetHit = IIf(abs(C-TP) < 0.01,1,Null);
  > Plot(C,"C",1,128);
  > Plot(Ti3( ReferenceArray,
  T3Periods ,T3Sensitivity),"ReferenceArray",1,1);
  > Plot(Ti3( TestArray, T3Periods ,T3Sensitivity),"TestArray",2,1);
  > PlotShapes(TargetHit*shapeHollowSquare,9,0,TP,0);
  > Plot(TP,"TP",4,1);
  >
  > --------------------------------------------------------------------
  --------
  > ----
  >
  >
  >
  >
  >
  >   -----Original Message-----
  >   From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
  >   Sent: Monday, October 25, 2004 3:04 PM
  >   To: amibroker@xxxxxxxxxxxxxxx
  >   Subject: [amibroker] Re: DT's Ct prediction for the Ti3
  >
  >
  >
  >   Herman,
  >   As I wrote in previous post, Ct is a function of Ti3Ct [and vice
  >   versa]
  >   In your example, Ti3C and Ti3H should be calculated separately, to
  >   avoid any confusion.
  >   The expected next bar Close Ct would be
  >
  >   Plot(C,"C",colorBlack,8);
  >   periods=5;s=0.7;f=2/(periods+1);R=1-f;
  >   //the Ti3H
  >   price=H;
  >   e1H=EMA(price,periods);
  >   e2H=EMA(e1H,Periods);
  >   e3H=EMA(e2H,Periods);
  >   e4H=EMA(e3H,Periods);
  >   e5H=EMA(e4H,Periods);
  >   e6H=EMA(e5H,Periods);
  >   c1=-s*s*s;
  >   c2=3*s*s+3*s*s*s;
  >   c3=-6*s*s-3*s-3*s*s*s;
  >   c4=1+3*s+s*s*s+3*s*s;
  >   Ti3H=c1*e6H+c2*e5H+c3*e4H+c4*e3H;
  >   //Plot(Ti3H,"Ti3H",1,1);
  >   //the Ti3C
  >   price=C;
  >   e1C=EMA(price,periods);
  >   e2C=EMA(e1C,Periods);
  >   e3C=EMA(e2C,Periods);
  >   e4C=EMA(e3C,Periods);
  >   e5C=EMA(e4C,Periods);
  >   e6C=EMA(e5C,Periods);
  >   Ti3C=c1*e6C+c2*e5C+c3*e4C+c4*e3C;
  >   //Plot(Ti3C,"Ti3C",2,1);
  >   Ti3Ct=Ti3H;//your condition:the next bar Ti3C is equal to todays
  Ti3H
  >   //the Ct as a function of Ti3Ct
  >   Ct=(Ti3Ct-R*(c1*(f^5*e1C+f^4*e2C+f^3*e3C+f^2*e4C+f*e5C+e6C)+c2*
  >   (f^4*e1C+f^3*e2C+f^2*e3C+f*e4C+e5C)+c3*(f^3*e1C+f^2*e2C+f*e3C+e4C)
  +c4*
  >   (f^2*e1C+f*e2C+e3C)))/(C1*f^6+C2*f^5+C3*f^4+C4*f^3) ;
  >   Plot(Ct,"Ct",colorRed,8);
  >
  >   For periods>10 the condition is quite rare.
  >   Dimitris
  >   --- In amibroker@xxxxxxxxxxxxxxx, "Herman van den Bergen"
  >   <psytek@xxxx> wrote:
  >   > In my requirements there is only one unknown, the next day Ct as
  >   the other
  >   > Ti3 was using the previous bar's value. The equation is
  solvable by
  >   > iteration however it is too slow for Real Time data, where in a
  >   backtests i
  >   > want to process 100,000 bars. The problem could also be stated,
  >   since both
  >   > Ti3s have the same value when crossing, and assigning arbitrary
  >   familiar
  >   > price arrays to Array1 and Array2, as:
  >   >
  >   > Ti3( ref(H,-1), period, sensitivity )  =  Ti3( C, period,
  >   sensitivity )
  >   >
  >   > and solving for C. In this equation C is the only unknown
  because H
  >   is
  >   > yesterday's known value. Your earlier solutions are close to
  this
  >   but i
  >   > haven't been able to modify them to this requirement. Note that
  >   periods and
  >   > sensitivities are the same on both sides of the equation.
  >   >
  >   > Best regards,
  >   > herman
  >   >
  >   >
  >   >   -----Original Message-----
  >   >   From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
  >   >   Sent: Monday, October 25, 2004 6:58 AM
  >   >   To: amibroker@xxxxxxxxxxxxxxx
  >   >   Subject: [amibroker] Re: DT's Ct prediction for the Ti3
  >   >
  >   >
  >   >
  >   >   To be more specific:
  >   >   Ti3t, the next bar Ti3 of an array, is ALWAYS a [known]
  function
  >   of
  >   >   the next bar array value arrayt.
  >   >   Arrayt is NOT ALWAYS a [known] function of the next bar Close
  Ct.
  >   >   Dimitris
  >   >   PS : If you could be more specific about array1, array2 we
  could
  >   >   probably come to some result...
  >   >   --- In amibroker@xxxxxxxxxxxxxxx, "Herman van den Bergen"
  >   >   <psytek@xxxx> wrote:
  >   >   > Thank you Dt.
  >   >   >
  >   >   > herman
  >   >   >   -----Original Message-----
  >   >   >   From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
  >   >   >   Sent: Monday, October 25, 2004 6:41 AM
  >   >   >   To: amibroker@xxxxxxxxxxxxxxx
  >   >   >   Subject: [amibroker] Re: DT's Ct prediction for the Ti3
  >   >   >
  >   >   >
  >   >   >
  >   >   >   Herman,
  >   >   >   There is no answer for this general question.
  >   >   >   Some arrays may be RevEnged [RSI, Ti3], some others not
  >   [StochD].
  >   >   >   The next bar RSI is a function of the next bar Close Ct,
  the
  >   next
  >   >   bar
  >   >   >   StochD is [unfortunately] a function of Ht, Lt and Ct.
  >   >   >   Dimitris
  >   >   >   --- In amibroker@xxxxxxxxxxxxxxx, "Herman van den Bergen"
  >   >   >   <psytek@xxxx> wrote:
  >   >   >   > Thank you DT, I tried this code but it requires that pb
  is
  >   >   greater
  >   >   >   than pa
  >   >   >   > and also it uses C in both Ti3s. I am looking for a
  sulution
  >   >   where
  >   >   >   pa==pb
  >   >   >   > and we use different price arrays.
  >   >   >   >
  >   >   >   > best regards,
  >   >   >   > herman
  >   >   >   >
  >   >   >   >
  >   >   >   >
  >   >   >   >
  >   >   >   >   -----Original Message-----
  >   >   >   >   From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
  >   >   >   >   Sent: Monday, October 25, 2004 1:57 AM
  >   >   >   >   To: amibroker@xxxxxxxxxxxxxxx
  >   >   >   >   Subject: [amibroker] Re: DT's Ct prediction for the
  Ti3
  >   >   >   >
  >   >   >   >
  >   >   >   >
  >   >   >   >   --- In amibroker@xxxxxxxxxxxxxxx, "Herman van den
  Bergen"
  >   >   >   >   <psytek@xxxx> wrote:
  >   >   >   >   > DT, I am not sure i understand the Ti3t... what i am
  >   trying
  >   >   to
  >   >   >   find
  >   >   >   >   out is
  >   >   >   >   > what tomorrows closing price would be to cause the
  >   crossing
  >   >   of
  >   >   >   two
  >   >   >   >   Ti3
  >   >   >   >   > functions.
  >   >   >   >
  >   >   >   >   Herman,
  >   >   >   >   this specific question is already in
  >   >   >   >   http://finance.groups.yahoo.com/group/amibroker-
  >   ts/files/A%
  >   >   20Ti3%
  >   >   >   >   20application/
  >   >   >   >   "Cross(Ti3a,Ti3b) predictions.txt"
  >   >   >   >   Dimitris
  >   >   >   >   For example:
  >   >   >   >   >
  >   >   >   >   > F1 = T3( Array1, 3, 0.8 );
  >   >   >   >   > F2 = T3( ref(Array2,-1), 3, 0.8 );
  >   >   >   >   >
  >   >   >   >   > Array1 and Array2 are two different arrays and
  could be
  >   any
  >   >   >   type of
  >   >   >   >   > indicator array. For development you can plug in
  any of
  >   the
  >   >   OHLC
  >   >   >   >   arrays, but
  >   >   >   >   > you cannot use the same price array for both
  function
  >   >   calles.
  >   >   >   >   > The Periods and Sensitivities are the same for both
  T3
  >   >   function
  >   >   >   >   calls.
  >   >   >   >   > F2 is based on yesterdays values, F1 is based on
  todays
  >   >   values.
  >   >   >   >   > I would like to calculate tomorrows value for Array1
  >   that
  >   >   would
  >   >   >   >   cause the
  >   >   >   >   > two functions to cross: cross(F1, F2).
  >   >   >   >   >
  >   >   >   >   > Do you think this is possible?
  >   >   >   >   >
  >   >   >   >   > thanks for you help DT!
  >   >   >   >   > herman
  >   >   >   >   >   -----Original Message-----
  >   >   >   >   >   From: DIMITRIS TSOKAKIS [mailto:TSOKAKIS@x...]
  >   >   >   >   >   Sent: Saturday, October 23, 2004 5:34 AM
  >   >   >   >   >   To: amibroker@xxxxxxxxxxxxxxx
  >   >   >   >   >   Subject: [amibroker] Re: DT's Ct prediction for
  the
  >   Ti3
  >   >   >   >   >
  >   >   >   >   >
  >   >   >   >   >
  >   >   >   >   >   Herman,
  >   >   >   >   >   Ti3t (the next bar Ti3) is a direct function of
  the
  >   next
  >   >   bar
  >   >   >   >   Close Ct.
  >   >   >   >   >   Ti3t=
  >   >   >   >   >   c1*(f*(f*(f*(f*(f*(f*Ct+(1-f)*e1)+
  >   >   >   >   >   (1-f)*e2)+(1-f)*e3)+(1-f)*e4)+(1-f)*e5)+(1-f)*e6)+
  >   >   >   >   >   c2*(f*(f*(f*(f*(f*Ct+(1-f)*e1)+(1-f)*e2)+(1-f)*e3)
  +
  >   >   >   >   >   (1-f)*e4)+(1-f)*e5)+
  >   >   >   >   >   c3*(f*(f*(f*(f*Ct+(1-f)*e1)+(1-f)*e2)+(1-f)*e3)+
  (1-f)
  >   *e4)+
  >   >   >   >   >   c4*(f*(f*(f*Ct+(1-f)*e1)+(1-f)*e2)+(1-f)*e3);
  >   >   >   >   >   If I understand your question, you want to solve
  Ct
  >   for
  >   >   any
  >   >   >   given
  >   >   >   >   >   Ti3t.
  >   >   >   >   >   Let me know and I will do it.
  >   >   >   >   >   Dimitris
  >   >   >   >   >   --- In amibroker@xxxxxxxxxxxxxxx, "Herman van den
  >   Bergen"
  >   >   >   >   >   <psytek@xxxx> wrote:
  >   >   >   >   >   > Hello,
  >   >   >   >   >   >
  >   >   >   >   >   > 'been looking at DT's Ct formula (nice work!) to
  >   predict
  >   >   >   where
  >   >   >   >   >   tomorrow's
  >   >   >   >   >   > Close will touch the Ti3 - see code below. Can
  >   anybody
  >   >   see a
  >   >   >   >   way to
  >   >   >   >   >   use this
  >   >   >   >   >   > formula to predict the Close of tomorrow needed
  to
  >   have
  >   >   the
  >   >   >   Ti3
  >   >   >   >   >   touch any
  >   >   >   >   >   > arbitrary point? For example a point on another
  >   >   indicator.
  >   >   >   >   >   >
  >   >   >   >   >   > My math is not up to this, any help would be
  >   >   appreciated!
  >   >   >   >   >   >
  >   >   >   >   >   > herman.
  >   >   >   >   >   >
  >   >   >   >   >   > p=3;s=0.84;f=2/(p+1);
  >   >   >   >   >   > // Ti3
  >   >   >   >   >   > e1=EMA(C,p);
  >   >   >   >   >   > e2=EMA(e1,p);
  >   >   >   >   >   > e3=EMA(e2,p);
  >   >   >   >   >   > e4=EMA(e3,p);
  >   >   >   >   >   > e5=EMA(e4,p);
  >   >   >   >   >   > e6=EMA(e5,p);
  >   >   >   >   >   > c1=-s*s*s;
  >   >   >   >   >   > c2=3*s*s+3*s*s*s;
  >   >   >   >   >   > c3=-6*s*s-3*s-3*s*s*s;
  >   >   >   >   >   > c4=1+3*s+s*s*s+3*s*s;
  >   >   >   >   >   > Ti3=c1*e6+c2*e5+c3*e4+c4*e3;
  >   >   >   >   >   > //The value of tomorrow´s Close Ct that touches
  >   >   tomorrow´s
  >   >   >   Ti3
  >   >   >   >   is
  >   >   >   >   >   > Ct=
  >   >   >   >   >   > (1-f)*((c1*f^5+c2*f^4+c3*f^3+c4*f^2)*e1+
  >   >   >   >   (c1*f^4+c2*f^3+c3*f^2+c4*f)
  >   >   >   >   >   *e2+(c1*f
  >   >   >   >   >   > ^3+c2*f^2+c3*f+c4*1)*e3+(c1*f^2+c2*f+c3*1)*e4+
  >   >   (c1*f+c2*1)
  >   >   >   >   *e5+c1*e6)/
  >   >   >   >   >   (1-(C1*f
  >   >   >   >   >   > ^6+C2*f^5+C3*f^4+C4*f^3)) ;//relation III
  >   >   >   >   >   > Plot(C,"Close",1,128);
  >   >   >   >   >   > Plot(Ti3,"Ti3",4,1);
  >   >   >   >   >   > Plot(Ct,"Ct",2,1);
  >   >   >   >   >
  >   >   >   >   >
  >   >   >   >   >
  >   >   >   >   >
  >   >   >   >   >
  >   >   >   >   >   Check AmiBroker web page at:
  >   >   >   >   >   http://www.amibroker.com/
  >   >   >   >   >
  >   >   >   >   >   Check group FAQ at:
  >   >   >   >   >
  >   http://groups.yahoo.com/group/amibroker/files/groupfaq.html
  >   >   >   >   >
  >   >   >   >   >
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  >   >   >   >   >
  >   >   >   >   > ----------------------------------------------------
  ----
  >   ----
  >   >   ----
  >   >   >   ----
  >   >   >   >   --------
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