TS Covar Function Error

[BlueHorseshoe 10]

Hello,

 

I've just been looking at the 'Covar' preset function in TS. It seems wrong to me. Here it is:

 

inputs:
Indep( numericseries ),
Dep( numericseries ),
Length( numericsimple ) ;

variables:
IndepMean( 0 ),
DepMean( 0 ),
Sum( 0 ) ;

if Length > 0 then 
begin
IndepMean = Average( Indep, Length ) ;
DepMean = Average( Dep, Length ) ;
Sum = 0 ;
for Value1 = 0 to Length - 1 
	begin
	Sum = Sum + ( Indep[Value1] - IndepMean ) * ( Dep[Value1] - DepMean ) ;
	end ;
Covar = Sum / Length ;
end
else
RaiseRunTimeError( "Length input to Covar function must be > 0" ) ;


{ ** Copyright (c) 2001 - 2010 TradeStation Technologies, Inc. All rights reserved. ** 
 ** TradeStation reserves the right to modify or overwrite this analysis technique 
    with each release. ** }

 

Am I correcting in thinking that where TS is using X Bar they should be using E, both in the IndepMean and DepMean calculation and in the summation process?

 

In other words, shouldn't IndepMean look something more like this . . .

For Value1=0 to Length-1 begin
Sum=Sum+(Price[Value1]*P[Price(Value1)]) ;
End ;
IndepMean=(1/Length)*Sum;

 

. . . where P is the probability of the occurence of Price[Value1] within a discrete probability distribution?

 

BlueHorseshoe

[onesmith 10]

This code is typical of the beginning step to test an idea. It plots the traditional indepMean next to my understanding of your alternative indepMean. The results don't necessarily prove or disprove anything. They provide information that enable altering the formula before proceeding to the next step. The alternative indepMean is considerably different than the concept of mean.

 

You didn't post a probability function so I used the built-in zProbability.

 

 

input: indep(c), len(20);
var: x(0), indepMean(0), bhsIndepMean(0);

indepMean=average(indep,len);

bhsIndepMean=0;
for x=0 to len-1 begin
   bhsIndepMean=bhsIndepMean+indep[x]*zprob(indep[x],len);
end;
bhsIndepMean=bhsIndepMean/len;

plot1(indepMean,"indepMean");
plot2(bhsIndepMean,"bhsIndepMean");

[BlueHorseshoe 10]

This code is typical of the beginning step to test an idea. It plots the traditional indepMean next to my understanding of your alternative indepMean. The results don't necessarily prove or disprove anything. They provide information that enable altering the formula before proceeding to the next step. The alternative indepMean is considerably different than the concept of mean.

 

You didn't post a probability function so I used the built-in zProbability.

 

 

That's helpful, thanks. Your understanding of what I am describing is correct - it's basically a weighted average where the weights are derived from a discrete probability distribution, pressumably gaussian.

 

My question is not so much how to implement this in EL (although that might have been my next question), as to whether the Covar function code provided by TS is 'wrong'?

 

The wikipedia definition of variance can be found here:

 

Variance - Wikipedia, the free encyclopedia

 

The notation uses the 'expected value' E or, seemingly interchangeably, Mu, rather than X bar arithmetic mean used by TS:

 

 

Any ideas as to whether one or the other of these is categorically correct?

 

Thanks for drawing my attention to the zProbability function in TS. I assume any similar process such as Ornstein-Uhlenbeck would be equally valid (or invalid!)?

 

BlueHorseshoe.

[onesmith 10]

I compared the results of the TS covar function to the output of an excel spreadsheet and also an online covariance calculator. Results of these 3 sources are identical.

[BlueHorseshoe 10]

I compared the results of the TS covar function to the output of an excel spreadsheet and also an online covariance calculator. Results of these 3 sources are identical.

 

Thanks, Onesmith. That pretty much answers my question then - never trust wikipedia!

 

Cheers,

 

BlueHorseshoe