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Howard,
Is there any reason to estimate, when we know the exact tomorrow´s
Close for an MA, EMA or DEMA cross ?
See in http://groups.yahoo.com/group/amibroker/files/
the Cross Predictions.txt for the respective formulas.
Dimitris Tsokakis
--- In amibroker@xxxxxxxxxxxxxxx, "howard bandy" <howardbandy@xxxx>
wrote:
> Greetings all – particularly Chuck –
>
> Here is a version that handles Exponential Moving Averages.
>
> If any of you find good uses for this technique, please feel free to
> let us all know about them.
>
> If there are other functions that would be valuable to compute
> crossover or prediction points for, let me know.
>
> Thanks,
> Howard
>
> //================================================
> //
> // Solve EMA Cross Point
> //
> // Howard Bandy
> // January 29, 2004
> //
> //!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> // This code is a variation of "Solve MA Cross Point".
> // In that version, the moving averages were Simple.
> // In this version, the moving averages are Exponential.
> //
> // Some background for those who have forgotten:
> // EMA needs only the previous value of the EMA,
> // the "alpha" value, and the next data point.
> // EMA(i) = alpha * Close(i) + (1 - alpha) * EMA(i-1)
> //
> // alpha = 2 / (N + 1), where N is the number of days
> // in the average.
> //
> // In our case, we want EMA(i+1), which is
> // alpha * Close(i+1) + (1-alpha) * EMA(i),
> // where the Close(i+1) is varied until we find
> // values that converge.
> //!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> //
> //
> // Load this routine into Indicator Builder and
> // apply it to any bar chart.
> //
> // This routine uses a binary search to compute
> // the value of the close
> // of the next bar such that two simple moving
> // averages will cross.
> //
> // It plots the price necessary and the change
> // from the most recent close.
> //
> // If MA1Length is shorter than MA2Length,
> // then MA1 is the faster moving average.
> // MA1 is plotted as a Blue line.
> // MA2 is plotted as a Green line.
> //
> // The computed price is plotted as a Red line.
> // The change from today's close to the
> // computed price is plotted as a Yellow line.
> //
> //!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> // In order to use this technique, you must be
> // able to compute the indicator you want to evaluate
> // for a variety of trial values for the next bar.
> //!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> //
> // This example makes use of the fact that the
> // new simple moving average is computed by
> // dropping off the oldest value and picking up the
> // newest value.
> //
>
> MA1Length = 3;
> MA2Length = 10;
> Longest = Max(MA1Length,MA2Length);
>
> Alpha1 = 2/(MA1Length+1);
> Alpha2 = 2/(MA2Length+1);
>
> MA1 = EMA(C,MA1Length);
> MA2 = EMA(C,MA2Length);
>
> // Establish initial values for the search.
> // Since the movign average will cross over at
> // only one point, we only need to be sure that
> // one startinging value is too high (above the
> // crossover point) and the other starting value
> // is too low (below the crossover point).
>
> MinC = 0.1 * C;
> MaxC = 10.0 * C;
>
> // Note on computational implications --
> // Assume the stock being processed has a Close
> // of $50.00. MaxC starts at $500.00, MinC at $5.00.
> // The range being searched is $495.00. The search stops
> // HighC and LowC are within $0.005. The ratio of $495.00
> // to $0.005 is 100000 to 1. Each search step cuts the
range
> // in half. So it will take about 17 steps to converge --
that
> // is 17 passes through the While loop for each bar in the
> // range being processed.
> // If MinC starts at 0.5 * C and MaxC starts at 2.0 * C,
> // the search is cut to 14 passes through the While loop.
> // If MinC and MaxC are 0.9 * C and 1.1 * C, 11 passes.
> // Increasing the stopping citerion from 0.005 to 0.02
> // cuts 2 passes off for any MinC and MaxC.
> //
> // All that is necessary is that MinC and MaxC bracket the
> // solution. In some cases, it might be advantageous to
use
> // a short routine that does not go through the
> // entire While loop can be used to pick MinC and MaxC
close
> // together, but with different signs for the "Difference".
> //
>
> // Declare the variables and initialize them
> MA1atCP1 = C; // MA1 at Ref(MA1,+1) using trial value of
Close.
> MA2atCP1 = C; // MA2 at Ref(MA2,+1) using trial value of
Close.
> MidC = C; // Next trial value of Close.
> ChgReq = 0; // Change in Close required for Crossover.
>
> // Of course, if we could use Ref(MA1,1), there would be no
> need
> // for all this. The difficulty is that we want to
repeatedly
> // change the value of the final element until we determine
> // the solution to the crossover.
>
> // Loop through all the bars
> for (i=Longest; i<BarCount; i++)
> {
> // Initialize the Low test value and compute
the
> indicators
> LowC[i] = MinC[i];
> MA1atCP1[i] = (Alpha1*LowC[i]) + (1-Alpha1) * MA1[i-1];
> MA2atCP1[i] = (Alpha2*LowC[i]) + (1-Alpha2) * MA2[i-1];
> DiffLowC[i] = MA1atCP1[i] - MA2atCP1[i];
>
> // Initialize the High test value and compute
the
> indicators
> HighC[i] = MaxC[i];
> MA1atCP1[i] = (Alpha1*HighC[i]) + (1-Alpha1) * MA1[i-1];
> MA2atCP1[i] = (Alpha2*HighC[i]) + (1-Alpha2) * MA2[i-1];
> DiffHighC[i] = MA1atCP1[i] - MA2atCP1[i];
>
> // Test to see if the two indicators have
> converged.
> // They probably have not yet, but we need a
value
> // at the first test of the loop.
> Difference[i] = abs(DiffLowC[i] - DiffHighC[i]);
>
> // Stay in the search loop until the upper
limit
> price
> // and lower limit price are within 0.005 (one
half
> cent in US)
> while (Difference[i] > 0.005)
> {
> // Pick the midpoint of LowC and
HighC
> to test next.
> MidC[i] = (LowC[i] + HighC[i]) / 2;
> // And compute the indicators
> MA1atCP1[i] = (Alpha1*MidC[i]) + (1-Alpha1)
*
> MA1[i-1];
> MA2atCP1[i] = (Alpha2*MidC[i]) + (1-Alpha2)
*
> MA2[i-1];
> DiffMidC[i] = MA1atCP1[i] - MA2atCP1[i];
>
> // Using the signs of the
differences,
> // decide whether to replace the
high
> test point
> // or the low test point by the new
> Middle test point
> SignMid[i] = DiffMidC[i] > 0.0;
> SignLow[i] = DiffLowC[i] > 0.0;
>
> if (SignMid[i] == SignLow[i])
> {
> // The sign of the
> difference at the LowC point and at the
> // MidC point are the
same.
> That means LowC and MidC are on
> // the same side of the
> crossover point we are looking for,
> // but MidC is closer.
> // So, replace Low with
> Middle
> LowC[i] = MidC[i];
> MA1atCP1[i] = (Alpha1*LowC[i]) +
> (1-Alpha1) * MA1[i-1];
> MA2atCP1[i] = (Alpha2*LowC[i]) +
> (1-Alpha2) * MA2[i-1];
> DiffLowC[i] = MA1atCP1[i] -
> MA2atCP1[i];
> }
> else
> {
> // Replace High with
Middle
> HighC[i] = MidC[i];
> MA1atCP1[i] = (Alpha1*HighC[i])
+
> (1-Alpha1) * MA1[i-1];
> MA2atCP1[i] = (Alpha2*HighC[i])
+
> (1-Alpha2) * MA2[i-1];
> DiffHighC[i] = MA1atCP1[i] -
> MA2atCP1[i];
>
> } // if-else
>
> // One of DiffLowC or DiffHighC has
> changed as the
> // search range has tightened, the
> other
> // remains as it was on the last
pass
> through the loop.
> // Compute the new difference
between
> the two.
> Difference[i] = abs(DiffLowC[i] - DiffHighC
[i]);
>
> } // while
>
>
> // After the loop, the value of MidC is the
value
> // at which the curves will cross
> MidC[i] = (LowC[i] + HighC[i])/2;
>
> // Limit MidC so that it plots reasonably
> MidC[i] = IIf(MidC[i]>1.25*C[i],1.25*C[i], MidC[i]);
> MidC[i] = IIf(MidC[i]<0.80*C[i],0.80*C[i], MidC[i]);
>
> // Compute the change required from the most
recent
> // Close to the next Close if crossover is to
> happen.
> ChgReq[i] = MidC[i] - C[i];
>
> } // for
>
> // Plot Close, MA1, MA2, and Computed Cross Point
> Plot(C,"C",colorBlack,styleCandle);
> Plot(EMA(C,MA1Length),"EMA1",colorBlue,styleLine);
> Plot(EMA(C,MA2Length),"EMA2",colorGreen,styleLine);
> Plot(MidC,"Computed Cross",colorRed,styleLine);
>
> // Plot Change Required to Cross
> Plot(ChgReq,"Change
Required",colorYellow,styleDots|styleLeftAxisScale);
> Plot(0.0,"",colorYellow,styleLine|styleLeftAxisScale);
>
> ---
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