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25 Aug 2009 07:27:07 -0000 X-Received: from unknown (69.147.108.202) by m5.grp.sp2.yahoo.com with QMQP; 25 Aug 2009 07:27:07 -0000 X-Received: from unknown (HELO bay0-omc3-s17.bay0.hotmail.com) (65.54.246.217) by mta3.grp.re1.yahoo.com with SMTP; 25 Aug 2009 07:27:07 -0000 X-Received: from hotmail.com ([65.54.175.77]) by bay0-omc3-s17.bay0.hotmail.com with Microsoft SMTPSVC(6.0.3790.3959); Tue, 25 Aug 2009 00:26:46 -0700 X-Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Tue, 25 Aug 2009 00:26:45 -0700 Message-ID: X-Received: from 202.156.14.203 by BAY104-DAV5.phx.gbl with DAV; Tue, 25 Aug 2009 07:26:40 +0000 X-Originating-Email: [dmoser71@hotmail.com] X-Sender: dmoser71@hotmail.com Message-Id: <9903957C-9B35-4C18-ABFC-3956320EC0D6@hotmail.com> To: MetaTrader_Experts_and_Indicators@yahoogroups.com In-Reply-To: <4A8DE9CD.7020806@lightpatch.com> References: <00a601ca21c4$5a23c240$0e6b46c0$@com> <4A8DE9CD.7020806@lightpatch.com> X-Mailer: Apple Mail (2.936) X-OriginalArrivalTime: 25 Aug 2009 07:26:45.0565 (UTC) FILETIME=[6680DED0:01CA2555] X-Originating-IP: 65.54.246.217 X-eGroups-Msg-Info: 1:12:0:0:0 From: David Moser X-Yahoo-Profile: dmoser71 X-eGroups-Approved-By: smokyatgroups via web; 25 Aug 2009 09:52:08 -0000 Sender: MetaTrader_Experts_and_Indicators@yahoogroups.com MIME-Version: 1.0 Mailing-List: list MetaTrader_Experts_and_Indicators@yahoogroups.com; contact MetaTrader_Experts_and_Indicators-owner@yahoogroups.com Delivered-To: mailing list MetaTrader_Experts_and_Indicators@yahoogroups.com List-Id: Precedence: bulk List-Unsubscribe: Date: Tue, 25 Aug 2009 15:26:30 +0800 Subject: [MT_E and I] Choppiness Index Indicator X-Yahoo-Newman-Property: groups-email-ff-m Reply-To: MetaTrader_Experts_and_Indicators@yahoogroups.com Content-Type: multipart/mixed; boundary="Apple-Mail-64-147567411" X-Antivirus: AVG for E-mail 8.5.409 [270.13.66/2325] --Apple-Mail-64-147567411 Content-Type: multipart/alternative; boundary="FAYLdbyQ0HjtYzuNQa8C5g7LBbkwYsIroGyNre9" --FAYLdbyQ0HjtYzuNQa8C5g7LBbkwYsIroGyNre9 Content-Type: text/plain; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable Dear Gman, Ben, Ron & Group, I recently read a few people in this forum asking about how to=20=20 determine if we are trending or ranging, and this indicator may just=20=20 give you insight you are looking for. I recently wrote this new=20=20 indicator called the Choppiness Index for a friend for us to do some=20=20 research on risk management in trading. My friend quoted from a book=20=20 he is currently reading, "the CI was designed by E.W. Driess, and it=20=20 was born out of ideas expressed in the Chaos theory and fractal=20=20 geometry work of Beno=EEt B. Mandelbrot. The primary insight it offers = =20 is that market prices are not random but exhibit a statistical=20=20 tendency to continue in the same direction over time." What this non-repainting indicator does in practical terms is define=20=20 periods of choppiness vs. periods of trending using a mathematical=20=20 model described at the below web site. Generally speaking: - CI values over 50 mean the instrument is more choppy than trending. - CI values below 50 mean the instrument is more trending than choppy. - CI values over 61.8 indicate strong choppiness. - CI values below 38.2 indicate strong trending. Obviously, there are different ways to interpret this indicator, and=20=20 calculating the CI over longer or shorter periods will make a=20=20 difference on how responsive or erratic the indicator's output=20=20 becomes, and should be experimented with to see how well different=20=20 settings fit into your particular trading strategy. I am already testing and incorporating its output into algorithms=20=20 where I need to filter for ranging or trending markets. I am=20=20 attaching screenshots of GBPUSD, M1, H4, W1 so you can see how it=20=20 might be useful in very short or very long term trading plans. I=20=20 added an alert function in case anyone wants to be notified when the=20=20 CI drops below or rises above programmable thresholds. The algorithm under the hood is described at this web site and an=20=20 excerpt follows: http://www.allbusiness.com/personal-finance/investing-trading-futures/40518= 4-1.html In the November 1991 issue of Technical Trader's Bulletin, Dreiss=20=20 explains how he interprets the CI: "Low readings in the CI correspond closely with the end of strong=20=20 impulsive movements either up or down, while high readings occur after=20=20 significant consolidations in the price. Extended periods of trendless=20=20 price movement are reflected in extended periods of above-average=20=20 readings of the CI. One might assume that markets with high CI should=20=20 be avoided and only markets with low CI should be traded. However, it=20=20 is more likely that one would want to avoid markets with constant=20=20 above-average CI and trade markets where the CI swings from one=20=20 extreme to the other." As with many technical indicators that look at past data, the CI=20=20 describes what has happened in the past, but isn't a crystal ball into=20=20 the future. It may provide, however, useful information about=20=20 impending changes in the current condition of the market. Dreiss says=20=20 "high CI readings can be used to indicate that a consolidation is=20=20 about to end and a position should be entered or a breakout=20=20 anticipated. (Since the CI reading has nothing to do with market=20=20 direction, it does not indicate in which direction to expect the=20=20 breakout, but that the breakout will probably be followed by a=20=20 significant move.) "Low CI readings can be used as a signal to take profits or tighten=20=20 stops in anticipation of a market reversal or consolidation, or in=20=20 some cases could be used to pick tops or bottoms." Regards, David Moser On Aug 21, 2009, at 8:26 AM, Ron Thompson wrote: > > After this post, I see you've asked for some ranging/trending=20=20 > indicators. > > That's good, because my very simple question for you was going to be: > > Can you please define "trending" and "ranging" :-) > > Ron > > > > Ben wrote: > >> >> Hi Group, >> >> I ran this EA for two days on a demo account and the result was=20=20 >> promising. >> Can some on in the group (Ron, if this is not too much to ask in=20=20 >> his busy schedule) to limit opening of its trades to trending times=20=20 >> only? >> Apparently, it does not perform in ranging market. >> >> Thanks >> Ben >> >> >> -----Original Message----- >> From: MetaTrader_Experts_and_Indicators@yahoogroups.com[mailto:MetaTrade= r_Experts_and_Indicators@yahoogroups.com=20 >> ] On Behalf Of Gman >> Sent: Tuesday, August 18, 2009 7:21 AM >> To: MetaTrader_Experts_and_Indicators@yahoogroups.com >> Subject: [MT_E and I] Promising indi... too good to be true? >> >> I can't remember where I found this indi, it was either forex-tsd=20=20 >> or forexfactory. >> >> It is based on the AC, AO and StdDv functions, and plots a red or=20=20 >> blue arrow on the chart. >> >> This indi does not repaint after the bar is closed, so what you see=20=20 >> on the chart is what you can trade at the open of the next bar=20=20 >> after a signal appears. >> >> It seems to work better on longer time frames, here I have looked=20=20 >> at H4. Should work equally well on any currency. >> >> It gives good results when the currency makes big moves. It=20=20 >> captures nearly all of the move, keeping you in the trade for as=20=20 >> long as the trend stays strong. >> >> In choppy or ranging times you will hit loss after loss, but mostly=20=20 >> they will be small losses. There can be significant drawdown (>100=20=20 >> pips) before price starts moving in your favour, so set lot size=20=20 >> accordingly. >> >> I made an EA which enters a trade at the open of the bar following=20=20 >> a signal, and closes when an opposite signal happens, and opens a=20=20 >> trade in the new signal direction. Despite how good the indi looks,=20=20 >> this is not profitable. >> >> Any ideas of how to improve this EA? >> >> The image attached shows how the EA trades. >> The indi paints the red and blue arrows. >> The yellow circle is where the EA opens and closes the trade. >> The blue and red lines and numbers show profitable and unprofitable=20=20 >> trades with pip amounts. >> The purple lines and numbers show maximum drawdown and pips from=20=20 >> the last position opened. >> >> >> >> >> >> >> >> >> > >=20 --FAYLdbyQ0HjtYzuNQa8C5g7LBbkwYsIroGyNre9 Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable  

Dear Gman, Ben, Ron & Group,

I recently read a few people in this forum asking about how to
determine if we are trending or ranging, and this indicator may just
give you insight you are looking for. I recently wrote this new
indicator called the Choppiness Index for a friend for us to do some
research on risk management in trading. My friend quoted from a book
he is currently reading, "the CI was designed by E.W. Driess, and it =
was born out of ideas expressed in the Chaos theory and fractal
geometry work of Beno=EEt B. Mandelbrot. The primary insight it offers is that market prices are not random but exhibit a statistical
tendency to continue in the same direction over time."

What this non-repainting indicator does in practical terms is define
periods of choppiness vs. periods of trending using a mathematical
model described at the below web site.

Generally speaking:
- CI values over 50 mean the instrument is more choppy than trending.
- CI values below 50 mean the instrument is more trending than choppy.
- CI values over 61.8 indicate strong choppiness.
- CI values below 38.2 indicate strong trending.

Obviously, there are different ways to interpret this indicator, and
calculating the CI over longer or shorter periods will make a
difference on how responsive or erratic the indicator's output
becomes, and should be experimented with to see how well different
settings fit into your particular trading strategy.

I am already testing and incorporating its output into algorithms
where I need to filter for ranging or trending markets. I am
attaching screenshots of GBPUSD, M1, H4, W1 so you can see how it
might be useful in very short or very long term trading plans. I
added an alert function in case anyone wants to be notified when the
CI drops below or rises above programmable thresholds.

The algorithm under the hood is described at this web site and an
excerpt follows:
http://www.allbusiness.com/personal-finance/= investing-trading-futures/405184-1.html

In the November 1991 issue of Technical Trader's Bulletin, Dreiss
explains how he interprets the CI:

"Low readings in the CI correspond closely with the end of strong impulsive movements either up or down, while high readings occur after significant consolidations in the price. Extended periods of trendless price movement are reflected in extended periods of above-average
readings of the CI. One might assume that markets with high CI should
be avoided and only markets with low CI should be traded. However, it
is more likely that one would want to avoid markets with constant
above-average CI and trade markets where the CI swings from one
extreme to the other."

As with many technical indicators that look at past data, the CI
describes what has happened in the past, but isn't a crystal ball into the future. It may provide, however, useful information about
impending changes in the current condition of the market. Dreiss says
"high CI readings can be used to indicate that a consolidation is about to end and a position should be entered or a breakout
anticipated. (Since the CI reading has nothing to do with market
direction, it does not indicate in which direction to expect the
breakout, but that the breakout will probably be followed by a
significant move.)

"Low CI readings can be used as a signal to take profits or tighten <= br> stops in anticipation of a market reversal or consolidation, or in
some cases could be used to pick tops or bottoms."

Regards,
David Moser

On Aug 21, 2009, at 8:26 AM, Ron Thompson wrote:

>
> After this post, I see you've asked for some ranging/trending
> indicators.
>
> That's good, because my very simple question for you was going to be:<= br> >
> Can you please define "trending" and "ranging" := -)
>
> Ron
>
>
>
> Ben wrote:
>
>>
>> Hi Group,
>>
>> I ran this EA for two days on a demo account and the result was <= br> >> promising.
>> Can some on in the group (Ron, if this is not too much to ask in =
>> his busy schedule) to limit opening of its trades to trending time= s
>> only?
>> Apparently, it does not perform in ranging market.
>>
>> Thanks
>> Ben
>>
>>
>> -----Original Message-----
>> From: MetaTrader_Experts_and_Indicators@yahoogroups.com= [mailto:MetaTrader_Experts_and_Indicators@yahoogroups.com
>> ] On Behalf Of Gman
>> Sent: Tuesday, August 18, 2009 7:21 AM
>> To: MetaTrader_Experts_and_Indicators@yahoogroups.com
>> Subject: [MT_E and I] Promising indi... too good to be true?
>>
>> I can't remember where I found this indi, it was either forex-tsd =
>> or forexfactory.
>>
>> It is based on the AC, AO and StdDv functions, and plots a red or =
>> blue arrow on the chart.
>>
>> This indi does not repaint after the bar is closed, so what you se= e
>> on the chart is what you can trade at the open of the next bar >> after a signal appears.
>>
>> It seems to work better on longer time frames, here I have looked =
>> at H4. Should work equally well on any currency.
>>
>> It gives good results when the currency makes big moves. It
>> captures nearly all of the move, keeping you in the trade for as =
>> long as the trend stays strong.
>>
>> In choppy or ranging times you will hit loss after loss, but mostl= y
>> they will be small losses. There can be significant drawdown (>= 100
>> pips) before price starts moving in your favour, so set lot size =
>> accordingly.
>>
>> I made an EA which enters a trade at the open of the bar following=
>> a signal, and closes when an opposite signal happens, and opens a =
>> trade in the new signal direction. Despite how good the indi looks= ,
>> this is not profitable.
>>
>> Any ideas of how to improve this EA?
>>
>> The image attached shows how the EA trades.
>> The indi paints the red and blue arrows.
>> The yellow circle is where the EA opens and closes the trade.
>> The blue and red lines and numbers show profitable and unprofitabl= e
>> trades with pip amounts.
>> The purple lines and numbers show maximum drawdown and pips from =
>> the last position opened.
>>
>>
>>
>>
>> <mime-attachment.jpeg>
>>
>>
>>
>> <mime-attachment.gif>
>
>

=20
=20=20
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=20=20
=20=20=20=20=20=20=20=20=20=20 For archives of Experts and Indicators from the MetaTrader Expert= s and Indicators Group, See h= ttp://www.ForexMT4.com/mt_yahoo/
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Recent Activity<= /div>
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Visit Your Group
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extern=20bool=20EnableAlertOnHigh=3Dfalse;=20=20=20//=20Alert=20setting=20= for=20entering=20time=20of=20choppiness=0D=0Aextern=20double=20= AlertHighVal=3D61.8;=20=20=20=20=20=20=20//=20Default=20value=20based=20= on=20fib=20numbers=0D=0Aextern=20bool=20EnableAlertOnLow=3Dfalse;=20=20=20= =20//=20Alert=20setting=20for=20entering=20time=20of=20trending=0D=0A= extern=20double=20AlertLowVal=3D38.2;=20=20=20=20=20=20=20=20//=20= Default=20value=20based=20on=20fib=20numbers=0D=0Aextern=20int=20= MaxCalcBars=3D1000;=20=20=20=20=20=20=20=20=20=20=20//=20Limit=20= calculations=20back=20this=20many=20bars=0D=0A=0D=0A//----=20indicator=20= buffers=0D=0Adouble=20ExtMapBuffer[];=0D=0Adouble=20StdDevHiBuffer[];=0D=0A= double=20StdDevLoBuffer[];=0D=0Adouble=20IntMapBuffer[];=0D=0Adouble=20= IntStdDevBuffer[];=0D=0A=0D=0A//----=20variables=0D=0Astring=20= TimeFrame;=0D=0Adatetime=20LastAlert=3D0;=0D=0A=0D=0A= //+------------------------------------------------------------------+=0D= =0A//|=20Custom=20indicator=20initialization=20function=20=20=20=20=20=20= =20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20|=0D=0A= //+------------------------------------------------------------------+=0D= =0Aint=20init()=0D=0A=20=20{=0D=0A=20=0D=0A=20=20=20IndicatorBuffers(5);=0D= =0A=20=20=20SetIndexStyle(0,DRAW_LINE);=0D=0A=20=20=20= SetIndexBuffer(0,ExtMapBuffer);=0D=0A=20=20=20= SetIndexStyle(1,DRAW_LINE);=0D=0A=20=20=20= SetIndexBuffer(1,StdDevHiBuffer);=0D=0A=20=20=20= SetIndexStyle(2,DRAW_LINE);=0D=0A=20=20=20= SetIndexBuffer(2,StdDevLoBuffer);=0D=0A=20=20=20= SetIndexBuffer(3,IntMapBuffer);=0D=0A=20=20=20= SetIndexBuffer(4,IntStdDevBuffer);=0D=0A=20=20=20=0D=0A=20=20=20if=20= (ChoppinessPeriod<2)=20ChoppinessPeriod=20=3D=202;=20=20=20//=20Any=20= lower=20and=20this=20indicator=20isn't=20relevant=0D=0A=20=20=20if=20= (SmoothingPeriod<1)=20SmoothingPeriod=20=3D=201;=20=20=20=20=20//=20= Avoid=20configuration=20errors=0D=0A=20=20=20if=20(StdDevPeriod<2)=20= StdDevPeriod=20=3D=202;=20=20=20=20=20=20=20=20=20=20=20//=20Any=20lower=20= and=20the=20Standard=20Deviation=20isn't=20relevant=0D=0A=20=20=20if=20= (MaxCalcBars>10000)=20MaxCalcBars=20=3D=2010000;=20=20=20=20=20//=20Any=20= higher=20and=20may=20adversely=20affect=20performance=20on=20multi-chart=20= setups=0D=0A=20=20=20=0D=0A=20=20=20= SetIndexDrawBegin(0,ChoppinessPeriod+SmoothingPeriod);=0D=0A=20=20=20= SetIndexDrawBegin(1,ChoppinessPeriod+SmoothingPeriod+StdDevPeriod);=0D=0A= =20=20=20= SetIndexDrawBegin(2,ChoppinessPeriod+SmoothingPeriod+StdDevPeriod);=0D=0A= =20=20=20=0D=0A=20=20=20string=20short_name=3D"Choppiness=20Index=20= ("+ChoppinessPeriod+","+SmoothingPeriod+","+StdDevPeriod+")";=0D=0A=20=20= =20IndicatorShortName(short_name);=0D=0A=0D=0A=20=20=20switch=20= (Period())=0D=0A=20=20=20=20=20{=0D=0A=20=20=20=20=20case=20=20=20=20=20= 1:=20TimeFrame=20=3D=20"M1";=20=20break;=0D=0A=20=20=20=20=20case=20=20=20= =20=205:=20TimeFrame=20=3D=20"M5";=20=20break;=0D=0A=20=20=20=20=20case=20= =20=20=2015:=20TimeFrame=20=3D=20"M15";=20break;=0D=0A=20=20=20=20=20= case=20=20=20=2030:=20TimeFrame=20=3D=20"M30";=20break;=0D=0A=20=20=20=20= =20case=20=20=20=2060:=20TimeFrame=20=3D=20"H1";=20=20break;=0D=0A=20=20=20= =20=20case=20=20=20240:=20TimeFrame=20=3D=20"H4";=20=20break;=0D=0A=20=20= =20=20=20case=20=201440:=20TimeFrame=20=3D=20"D1";=20=20break;=0D=0A=20=20= =20=20=20case=2010080:=20TimeFrame=20=3D=20"W1";=20=20break;=0D=0A=20=20=20= =20=20case=2043200:=20TimeFrame=20=3D=20"MN";=20=20break;=0D=0A=20=20=20= }=0D=0A=0D=0A//----=20initial=20zero=0D=0A=20=20=20for(int=20= i=3D0;i<=3DBars;i++)=20ExtMapBuffer[i]=3D0;=20=20//=20Smoothed=20&=20= visible=20main=20indicator=20line=0D=0A=20=20=20for(i=3D0;i<=3DBars;i++)=20= StdDevHiBuffer[i]=3D0;=20=20=20=20//=20Upper=20StdDev=20band,=20visible=0D= =0A=20=20=20for(i=3D0;i<=3DBars;i++)=20StdDevLoBuffer[i]=3D0;=20=20=20=20= //=20Lower=20StdDev=20band,=20visible=0D=0A=20=20=20for(i=3D0;i<=3DBars;i+= +)=20IntMapBuffer[i]=3D0;=20=20=20=20=20=20//=20Raw=20CI,=20not=20= smoothed,=20not=20visible=0D=0A=20=20=20for(i=3D0;i<=3DBars;i++)=20= IntStdDevBuffer[i]=3D0;=20=20=20//=20Raw=20StdDev=20of=20Smoothed=20&=20= visible=20main=20indicator=20line=20(ExtMapBuffer)=0D=0A=0D=0A=20=20=20= return(0);=0D=0A=20=20}=0D=0A= //+------------------------------------------------------------------+=0D= =0A//|=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20= =20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20= =20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20=20|=0D=0A= //+------------------------------------------------------------------+=0D= =0Aint=20start()=0D=0A=20=20{=0D=0A=20=20int=20= counted_bars=3DIndicatorCounted();=0D=0A=20=20int=20z,limit;=0D=0A=20=20= double=20bufferTemp1,=20bufferTemp2;=0D=0A=0D=0A=20=20if=20= (counted_bars<0)=20return(-1);=20=0D=0A=20=20if=20(counted_bars>0)=20= counted_bars--;=20=0D=0A=20=20limit=3DBars-counted_bars;=0D=0A=20=20if=20= (limit>MaxCalcBars)=20limit=3DMaxCalcBars;=0D=0A=20=20=0D=0A=20=20for=20= (int=20i=3Dlimit-1;=20i>=3D0;=20i--)=20=0D=0A=20=20=20=20{=0D=0A=20=20=20= =20IntMapBuffer[i]=20=3D=20ChoppinessIndex(ChoppinessPeriod,i);=0D=0A=20=20= =20=20bufferTemp1=20=3D=200;=0D=0A=20=20=20=20for(int=20j=3D0;=20= jAlertHighVal)=20&&=20(ExtMapBuffer[2]AlertLowVal))=0D=0A= =20=20=20=20=20=20=20=20=20=20{=0D=0A=20=20=20=20=20=20=20=20=20=20= LastAlert=20=3D=20Time[0];=20//=20No=20more=20alerts=20on=20the=20= current=20bar=0D=0A=20=20=20=20=20=20=20=20=20=20= Alert(Symbol()+","+TimeFrame+":Choppiness=20less=20than=20= "+DoubleToStr(AlertLowVal,1));=0D=0A=20=20=20=20=20=20=20=20=20=20}=0D=0A= =0D=0A=20=20return(0);=0D=0A=20=20}=0D=0A=20=20=0D=0A=20=20=0D=0Adouble=20= ChoppinessIndex(int=20period,=20int=20bar)=0D=0A=20=20{=0D=0A=20=20=20=20= double=20Low0=20=3D=200,=20High0=20=3D=200,=20Close1=20=3D=200;=0D=0A=20=20= =20=20double=20TrueRangeLow=20=3D=200,=20TrueRangeHigh=20=3D=200,=20= TrueRangeSum=20=3D=200,=20Input=20=3D=200;=0D=0A=20=20=20=20double=20= PeriodTrueRangeLow=20=3D=20999999999,=20PeriodTrueRangeHigh=20=3D=200,=20= PeriodTrueRange=20=3D=200;=0D=0A=0D=0A=20=20=20=20for(int=20k=3Dbar;=20= kClose1)=20TrueRangeHigh=20=3D=20= High0;=20else=20TrueRangeHigh=20=3D=20Close1;=0D=0A=20=20=20=20=20=20=0D=0A= =20=20=20=20=20=20if=20(TrueRangeLow=20PeriodTrueRangeHigh)=20PeriodTrueRangeHigh=20=3D=20= TrueRangeHigh;=20//=20find=20true=20high=20of=20period=0D=0A=0D=0A=20=20=20= =20=20=20TrueRangeSum=20+=3D=20TrueRangeHigh;=0D=0A=20=20=20=20=20=20= TrueRangeSum=20-=3D=20TrueRangeLow;=0D=0A=20=20=20=20}=0D=0A=0D=0A=20=20=20= =20PeriodTrueRange=20=3D=20PeriodTrueRangeHigh=20-=20PeriodTrueRangeLow;=0D= =0A=20=20=20=20if=20(PeriodTrueRange=3D=3D0)=20PeriodTrueRange=20=3D=20= MathPow(10,=20-12);=20//=20avoid=20possibility=20of=20division=20by=20= zero=0D=0A=20=20=20=20Input=20=3D=20TrueRangeSum=20/=20PeriodTrueRange;=0D= =0A=20=20=20=20return=20((logN(Input,=2010,=20MathPow(10,=20-12))=20/=20= logN(period,=2010,=20MathPow(10,=20-12)))=20*=20100);=0D=0A=20=20}=0D=0A=20= =20=0D=0A=0D=0Adouble=20logN(double=20x,=20double=20base,=20double=20= epsilon)=0D=0A=20=20{=0D=0A=20=20=20=20double=20integer=20=3D=200.0;=0D=0A= =20=20=20=20if=20((x=20<=201)=20||=20(base=20<=201))=20return(0);=0D=0A=0D= =0A=20=20=20=20while=20(x=20<=201)=0D=0A=20=20=20=20{=0D=0A=20=20=20=20=20= =20integer=20-=3D=201;=0D=0A=20=20=20=20=20=20x=20*=3D=20base;=0D=0A=20=20= =20=20}=0D=0A=20=20=0D=0A=20=20=20=20while=20(x=20>=3D=20base)=0D=0A=20=20= =20=20{=0D=0A=20=20=20=20=20=20integer=20+=3D=201;=0D=0A=20=20=20=20=20=20= x=20/=3D=20base;=0D=0A=20=20=20=20}=0D=0A=20=20=0D=0A=20=20=20=20double=20= partial=20=3D=200.5;=0D=0A=20=20=20=20x=20*=3D=20x;=0D=0A=20=20=20=20= double=20decimal=20=3D=200.0;=0D=0A=0D=0A=20=20=20=20while=20(partial=20= >=20epsilon)=0D=0A=20=20=20=20{=0D=0A=20=20=20=20=20=20if=20(x=20>=3D=20= base)=0D=0A=20=20=20=20=20=20{=0D=0A=20=20=20=20=20=20=20=20decimal=20+=3D= =20partial;=0D=0A=20=20=20=20=20=20=20=20x=20=3D=20x=20/=20base;=0D=0A=20= =20=20=20=20=20}=0D=0A=20=20=20=20=20=20partial=20*=3D=200.5;=0D=0A=20=20= =20=20=20=20x=20*=3D=20x;=0D=0A=20=20=20=20}=0D=0A=20=20=20=20=0D=0A=20=20= =20=20return=20(integer=20+=20decimal);=0D=0A=20=20}=20=0D=0A=0D=0A=0D=0A= double=20StdDev(int=20shift,=20int=20samples)=0D=0A=20=20{=0D=0A=20=20= double=20x0=3D0,=20x1=3D0,=20x2=3D0;=0D=0A=20=20for=20(int=20m=3D0;=20= m