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Thanks, Anthony. I knew what r-squared was; I was just confused by the AFL
code that correlated C with ref(C,-5). You answered my question perfectly. The
latter compares only 2 data points (I don't know why anyone would want to do
that; the correlation of 2 points will always be perfect!), whereas you have to
use cum(1) to look at the strength of a trend over a number of bars. Thanks
again.
AV
<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
Anthony Faragasso
To: <A title=amibroker@xxxxxxxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Friday, February 14, 2003 10:20
PM
Subject: Re: [amibroker] r-squared and
regression analysis
Al,The R2 indicator measures how closely prices
follow a linear regressiontrendline. This indicates the strength of
the trend...the more closelyprices move in a linear relationship with the
passing of time, thestronger the trend.It is helpful to consider
the R2 in relation to linear regression slope.While linear regression
slope gives you the general direction of thetrend ( whether positive or
negative ) , R2 gives you the strength ofthe trend. A high R2 value can be
associated with a high positive ornegative linear regression
slope.Although it is useful to know the R2 value, ideally, you should
use R2in tandem with linear regression slope. High R2 values
accompanied by alarge linear regression slope value are of most interest
to traders.There is more.....if you
want*********************************************************Answering
your questions:1. Yes. to the first part....2nd part you are
correlating the close tothe close nPeriods ago.( only 2 data points
)example, load into indicator builder:R_Squared=
Correlation(Cum(1),C,5)^2;R2=Correlation(C,Ref(C,-5),5)^2;Plot(r_squared,"r_squared",colorRed,styleLine);Plot(r2,"r2",colorYellow,styleLine);2.
Yes , I am correlating the closing price of the NDX to the closingprice of
"whatever ticker", over n Periods. Which
will tell me how closely the " whatever ticker" is followingthe price
movement of the NDX. therefore, this might
be one way to locate stocks to trade...the higher the R2value the more
closely the ticker is following the NDX and the
lower the R2 value the more the ticker is moving in theopposite direction
...example...select QQQ's as your ticker....and load the following
intoindicator builder...since the QQQ's track the NDX there will be a
highR2 value..../***Base Market************/Mkt="^ndx";//Must
be enclosed in
"....."Quotations.P=Foreign(Mkt,"C",1);/**************************/Periods=14;//Set
the period of
Observation/***R-Squared*****************/R2=Correlation(P,C,Periods)^2;/*****************************/AnthonyAvcinci
wrote:> Anthony, What I was doing was simply citing what the help
file gave as> an example of using the correlation function to establish
a trend of> closing prices over a period of time. Your explanation
probably> reflects my poor understanding of the cum(1) function. When
you write> R2 = Correlation(cum(1),C,14)^2, does this mean you are
correlating> all the closing prices over the last 14 days (in other
words, closing> price as a function of time)? If so, how does this
statement differ> from R2 = Correlation(C,ref(C,-pds),pds)^2? In your
next R2 statement,> you wrote R2 = (P, C, periods)^2, where P had been
assigned to the> closing price of the NDX index. So, it looks like you
are correlating> the price of the index with the closing price of
something else. I> don't know what all the other stuff about alpha and
beta have to do> with that. I guess I'm having difficulty understanding
your second R2> statement. Can you enlighten me a bit? Thanks a lot.
AV>> ----- Original Message
-----> From: Anthony
Faragasso> To:
amibroker@xxxxxxxxxxxxxxx> Sent: Friday,
February 14, 2003 8:49 PM> Subject: Re:
[amibroker] r-squared and regression
analysis>
Al,>> Here is
Metastocks:>> The following is the
formula for Metastocks r-squared:>
r_squared
=Pwr(Corr(Cum(1),C,14,0),2)>> AFL
Translation:>>
R_squared=correlation(cum(1),C,14)^2;>>
********************************************>>
The formula I posted is from my Alpha and Beta
indicators> located in
the>
library.> <A
href="">http://www.amibroker.com/library/formula.php?id=157>>
//Alpha AND Beta Indicators> //Ver.1.00,
2/10/02> //coded by Anthony
Faragasso> //e-mail:
ajf1111@xxxxxxxx>> //Insert your
Stock_index,Composite_index,
S&P,etc.> //as the **Base
Market**.>>
MaxGraph=5;>> /***Base
Market************/> Mkt="^ndx";//Must be
enclosed in "....."Quotations.>
P=Foreign(Mkt,"C",1);>
/**************************/>>
Periods=14;//Set the period of
Observation>>
//****Beta***********************/>>
Beta=(( Periods * Sum(ROC( C,1) * ROC(P,1),Periods ))
-> (Sum(ROC(C,1),Periods) * Sum(ROC(
P,1),Periods))) /> ((Periods
*> Sum((ROC(P,1)^2 ),Periods)) -
(Sum(ROC(P,1 ),Periods)^2 ));>
/******************************************/>>
//*****Alpha*********************/>>
Alpha=(Sum(ROC( C,1) ,Periods) - ( Beta ) * Sum( ROC(
P,1)> ,Periods )
)> /
Periods;>
/******************************************/>>
/***R-Squared*****************/>
R2=Correlation(P,C,Periods)^2;>
/************************************/>
Graph0=Beta;>
Graph0Style=1;>
Graph1=Alpha;>>
/Graph1=(LastValue(Highest(Graph0))/LastValue(Highest(Graph1)))>
*>
Graph1;>
Graph1Style=1;>> /**R_squared
graphing*****/>
Graph2=r2;>
Graph2Style=1;>
Graph2Color=7;>
/*************************/>
Title=Name()+" "+"ALPHA>>
+EncodeColor(colorBlue)+"("+WriteVal(Alpha,format=1.2)+")"+">>
"+EncodeColor(colorBlack)+" BETA>
"+EncodeColor(colorRed)+"("+WriteVal(Beta,format=1.2)+")"+">
"+EncodeColor(colorBlack)+" R_SQUARED>
"+EncodeColor(colorYellow)+"("+WriteVal(r2,format=1.2)+")";>>
/**Notes***/> //You've got to start with
r-squared, which is an> //indicator of
the validity of the beta AND alpha>
//measures. Because the r-squared measures just
how> //closely the Stock OR fund tracks
the> //index with which it is being
compared.>> //An r-squared of 1.0
indicates> //A perfect match. AND, in
that case, you can> //trust that the beta
AND alpha measures are> //valid, too.
But, the lower the r-squared, the less>
//reliable beta AND alpha measures
are.>> //"[Betas and alphas on] a
Stock or fund with an r-squared>
that's below> //0.50 are completely
meaningless.>> //Assuming the
r-squared is, say, 0.75 OR higher, you
can> move on to
the>
//beta.>>>> Avcinci
wrote:>> > Anthony, Shouldn't
it be: R2 = Correlation(P,> >
ref(P,-periods),periods)^2; ? Al V.>
>> >
----- Original Message ----->
> From: Anthony
Faragasso>
> To:
amibroker@xxxxxxxxxxxxxxx>
> Sent: Friday, February 14, 2003 8:10
PM> >
Subject: Re: [amibroker] r-squared and
regression>
analysis>
> /***Base
Market************/>
> Mkt="^ndx";//Must be enclosed in
"....."Quotations.>
> P=Foreign(Mkt,"C",1);//Base
market>
>> >
Periods=14;//Set the period of
Observation>
>> >
/***R-Squared*****************/>
>
R2=Correlation(P,C,Periods)^2;>
>>
>>
>> >
"sidleysh " wrote:>
>> >
> Does anyone know how to construct r-squared in
AB?>
There> >
is an r->
> > squared function in MetaStock, and I
desperately> need
it> > to
construct>
> > and adaptive MA based on the AT3 from
T&A>
> >>
> >>
>
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