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Greetings –
Included in this message is <span
class=GramE>afl code which determines the price at which two
simple moving averages will crossover.
Thanks,
Howard
//==============================================
// Solve MA
Cross Point
//
// Howard
Bandy
// <st1:date
Month="1" Day="29" Year="2004">January 29, 2004<font
size=2 face=Arial>
//
// Load this
routine into Indicator Builder and
// apply it to
any bar chart.
//
// <span
class=GramE>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.
//
// <span
class=GramE>The computed price is plotted as a Red line.
// <span
class=GramE>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.
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//
// <span
class=GramE>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);
MA1 = MA(C,MA1Length);
MA2 = MA(C,MA2Length);
// <span
class=GramE>Establish initial values for the search.
// <span
class=GramE>Since the movign average will cross
over at
// only one
point, we only need to be sure that
// one <span
class=SpellE>startinging value is too high (above the
// crossover
point) and the other starting value
// is too low
(below the crossover point).
<span
>MinC<font
size=2 face=Arial> = 0.1 * C;
<span
>MaxC<font
size=2 face=Arial> = 10.0 * C;
// Note on
computational implications --
// <span
class=GramE>Assume the stock being processed has a Close
// of
$50.00. MaxC
starts at $500.00, MinC at $5.00.
// <span
class=GramE>The range being searched is $495.00.<span
> The search stops
// <span
class=SpellE>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 <span
class=SpellE>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 <span
class=SpellE>MinC and MaxC are 0.9 * C and 1.1
* C, 11 passes.
// <span
class=GramE>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.<span
> 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 <span
class=SpellE>MaxC close
// together,
but with different signs for the "Difference".
//
// <span
class=GramE>Declare the variables and initialize them
MA1atCP1 = C; //<span
> MA1 at Ref(MA1,+1)
using trial value of Close.
MA2atCP1 = C; //<span
> MA2 at Ref(MA2,+1)
using trial value of Close.
<span
>MidC<font
size=2 face=Arial> = C;<span
> // Next trial value of Close.
<span
>ChgReq<font
size=2 face=Arial> = 0;<span
> // 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
<span
>for<font
size=2 face=Arial> (<span
class=SpellE>i=Longest; i<<span
class=SpellE>BarCount; i++)
{
//<span
> Initialize the Low test value and
compute the indicators
<span
class=SpellE>LowC[i] = MinC[<span
class=SpellE>i];
<span
class=GramE>MA1atCP1[i] = (MA1Length*MA1[<span
class=SpellE>i]-C[i-(MA1Length-1)]+<span
class=SpellE>LowC[i])/MA1Length;
<span
class=GramE>MA2atCP1[i] = (MA2Length*MA2[<span
class=SpellE>i]-C[i-(MA2Length-1)]+<span
class=SpellE>LowC[i])/MA2Length;
<span
class=SpellE>DiffLowC[i] = MA1atCP1[<span
class=SpellE>i] - MA2atCP1[i];
//<span
> Initialize the High test value and
compute the indicators
<span
class=SpellE>HighC[i] = MaxC[<span
class=SpellE>i];
<span
class=GramE>MA1atCP1[i] = (MA1Length*MA1[<span
class=SpellE>i]-C[i-(MA1Length-1)]+<span
class=SpellE>HighC[i])/MA1Length;
<span
class=GramE>MA2atCP1[i] = (MA2Length*MA2[<span
class=SpellE>i]-C[i-(MA2Length-1)]+<span
class=SpellE>HighC[i])/MA2Length;
<span
class=SpellE>DiffHighC[i] = MA1atCP1[<span
class=SpellE>i] - MA2atCP1[i];
//<span
> Test to see if the two indicators have
converged.
//<span
> They probably
have not yet, but we need a value
//<span
> at the first test of the loop.
Difference[<span
class=SpellE>i] = abs(DiffLowC[<span
class=SpellE>i] - DiffHighC[<span
class=SpellE>i]);
//<span
> Stay in the search loop until the
upper limit price
//<span
> and lower limit price are within 0.005
(one half cent in US)
<span
class=GramE>while (Difference[i] > 0.005)
{
//<span
> Pick the midpoint of <span
class=SpellE>LowC and HighC to test next.
<span
class=SpellE>MidC[i] = (LowC[<span
class=SpellE>i] + HighC[i])
/ 2;
//<span
> And compute
the indicators
<span
class=GramE>MA1atCP1[i] = (MA1Length*MA1[<span
class=SpellE>i]-C[i-(MA1Length-1)]+<span
class=SpellE>MidC[i])/MA1Length;
<span
class=GramE>MA2atCP1[i] = (MA2Length*MA2[<span
class=SpellE>i]-C[i-(MA2Length-1)]+<span
class=SpellE>MidC[i])/MA2Length;
<span
class=SpellE>DiffMidC[i] = MA1atCP1[<span
class=SpellE>i] - MA2atCP1[i];
//<span
> Using the
signs of the differences,
//<span
> decide whether to replace the high
test point
//<span
> or the low test point by the new
Middle test point
<span
class=SpellE>SignMid[i] = DiffMidC[<span
class=SpellE>i] > 0.0;
<span
class=SpellE>SignLow[i] = DiffLowC[<span
class=SpellE>i] > 0.0;
<span
class=GramE>if (SignMid[i]
== SignLow[i])
{
//<span
> The sign of
the difference at the LowC point and at the
//<span
> MidC point
are the same. That means <span
class=SpellE>LowC and MidC are on
//<span
> the same side of the crossover point
we are looking for,
//<span
> but MidC is
closer.
//<span
> So, replace
Low with Middle
<span
class=SpellE>LowC[i] = MidC[<span
class=SpellE>i];
<span
class=GramE>MA1atCP1[i] = (MA1Length*MA1[<span
class=SpellE>i]-C[i-(MA1Length-1)]+<span
class=SpellE>LowC[i])/MA1Length;
<span
class=GramE>MA2atCP1[i] = (MA2Length*MA2[<span
class=SpellE>i]-C[i-(MA2Length-1)]+<span
class=SpellE>LowC[i])/MA2Length;
<span
class=SpellE>DiffLowC[i] = MA1atCP1[<span
class=SpellE>i] - MA2atCP1[i];
}
<span
class=GramE>else
{
//<span
> Replace High with Middle
<span
class=SpellE>HighC[i] = MidC[<span
class=SpellE>i];
<span
class=GramE>MA1atCP1[i] = (MA1Length*MA1[<span
class=SpellE>i]-C[i-(MA1Length-1)]+<span
class=SpellE>HighC[i])/MA1Length;
<span
class=GramE>MA2atCP1[i] = (MA2Length*MA2[<span
class=SpellE>i]-C[i-(MA2Length-1)]+<span
class=SpellE>HighC[i])/MA2Length;
<span
class=SpellE>DiffHighC[i] = MA1atCP1[<span
class=SpellE>i] - MA2atCP1[i];
}<span
> // if-else
//<span
> One of DiffLowC
or DiffHighC has changed as the
//<span
> search range has tightened, the other
//<span
> remains as it was on the last pass
through the loop.
//<span
> Compute the new difference between the
two.
Difference[<span
class=SpellE>i] = abs(DiffLowC[<span
class=SpellE>i] - DiffHighC[<span
class=SpellE>i]);
}<span
> // while
//<span
> After the
loop, the value of MidC is the value
//<span
> at which the curves will cross
<span
class=SpellE>MidC[i] = (LowC[<span
class=SpellE>i] + HighC[i])/2;
//<span
> Limit MidC
so that it plots reasonably
<span
class=SpellE>MidC[i] = <span
class=GramE>IIf(MidC[<span
class=SpellE>i]>1.25*C[i],1.25*C[<span
class=SpellE>i], MidC[i]);
<span
class=SpellE>MidC[i] = <span
class=GramE>IIf(MidC[<span
class=SpellE>i]<0.80*C[i],0.80*C[<span
class=SpellE>i], MidC[i]);
//<span
> Compute the change required from the
most recent
//<span
> Close to the next Close if crossover
is to happen.
<span
class=SpellE>ChgReq[i] = MidC[<span
class=SpellE>i] - C[i];
} //<span
> for
// Plot Close,
MA1, MA2, and Computed Cross Point
Plot(C,"C",colorBlack,styleCandle);
<span
>Plot(<font
size=2 face=Arial>MA(C,MA1Length),"MA1",colorBlue,styleLine);
<span
>Plot(<font
size=2 face=Arial>MA(C,MA2Length),"MA2",colorGreen,styleLine);
<span
>Plot(<span
class=SpellE>MidC,"Computed<span
> Cross",colorRed,styleLine);
// Plot Change
Required to Cross
<span
>Plot(<span
class=SpellE>ChgReq,"Change<span
> Required",colorYellow,styleDots|styleLeftAxisScale);
<span
>Plot(<font
size=2 face=Arial>0.0,"",colorYellow,styleLine|styleLeftAxisScale);
Send BUG REPORTS to bugs@xxxxxxxxxxxxx
Send SUGGESTIONS to suggest@xxxxxxxxxxxxx
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