Leeds, Mark (IED)
2007-May-08 17:25 UTC
[R] statistics/correlation question NOT R question
This is not an R question but if anyone can help me, it's much
appreciated.
Suppose I have a series ( stationary ) y_t and a series x_t ( stationary
)and x_t has variance sigma^2_x and epsilon is normal
(0, sigma^2_epsilon )
and the two series have the relation
y_t = Beta*x_t + epsilon
My question is if there are particular values that sigma^2_x and
sigma^2_epsilon have to take in order for corr(x_t,y_t) to equal Beta ?
I attempted to figure this out using two different methods and in one
case I end up involving sigma^2_epsilon and in the other I don't
and I'm not sure if either method is correct. I think I need to use
results form the conditional bivariate normal but i'm really not sure.
Also, it's not a homework problem because I am too old to have homework.
Thanks for any insights/solutions.
--------------------------------------------------------
This is not an offer (or solicitation of an offer) to buy/se...{{dropped}}
Mark, I suppose you make the usual assumptions, ie. E[x]=0, E[x*epsilon]=0, the correlation is just simply, corr(x,y) = beta * ( var(x) / var(y) ) And you could get var(y) from var(x) and var(epsilon). HTH. Horace>>> "Leeds, Mark (IED)" <Mark.Leeds at morganstanley.com> 5/8/2007 10:25:11 AM >>>This is not an R question but if anyone can help me, it's much appreciated. Suppose I have a series ( stationary ) y_t and a series x_t ( stationary )and x_t has variance sigma^2_x and epsilon is normal (0, sigma^2_epsilon ) and the two series have the relation y_t = Beta*x_t + epsilon My question is if there are particular values that sigma^2_x and sigma^2_epsilon have to take in order for corr(x_t,y_t) to equal Beta ? I attempted to figure this out using two different methods and in one case I end up involving sigma^2_epsilon and in the other I don't and I'm not sure if either method is correct. I think I need to use results form the conditional bivariate normal but i'm really not sure. Also, it's not a homework problem because I am too old to have homework. Thanks for any insights/solutions. -------------------------------------------------------- This is not an offer (or solicitation of an offer) to buy/se...{{dropped}} ______________________________________________ R-help at stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
gyadav at ccilindia.co.in
2007-May-09 08:58 UTC
[R] statistics/correlation question NOT R question
Hi Horace and Mark
@@@ i myself know that this may be of little help but then also i am going
with this. Secondly the in the solution by Horace if corr(x, y) is beta
then
it implies that var(x) = var(y). Is that you want Mark. Well what i did i
am writing it down hereas under, may be its wrong.Please comment
var(y_t) = var(beta * x_t) + e_t)
=> var(y_t) = beta * var(x_t) + var(e_t) + cov(beta * x_t , e_t)
as cov(beta * x_t , e_t) = 0 hence
var(y_t) = beta * var(x_t) + var(e_t)............(i)
then
corr(x_t, y_t) = beta = cov(x_t, y_t)/ (sigma_x * sigma_y)
................ (ii)
further E[y_t] = beta * E[x_t] + E[e_t].........as E[e_t] = 0 hence
beta = E[y_t] / E[x_t]............(iii)
Now what to do ???
Mark, I suppose you make the usual assumptions, ie. E[x]=0,
E[x*epsilon]=0, the correlation is just simply,
corr(x,y) = beta * ( var(x) / var(y) )
And you could get var(y) from var(x) and var(epsilon).
HTH.
Horace
This is not an R question but if anyone can help me, it's much
appreciated.
Suppose I have a series ( stationary ) y_t and a series x_t ( stationary
)and x_t has variance sigma^2_x and epsilon is normal
(0, sigma^2_epsilon )
and the two series have the relation
y_t = Beta*x_t + epsilon
My question is if there are particular values that sigma^2_x and
sigma^2_epsilon have to take in order for corr(x_t,y_t) to equal Beta ?
I attempted to figure this out using two different methods and in one
case I end up involving sigma^2_epsilon and in the other I don't
and I'm not sure if either method is correct. I think I need to use
results form the conditional bivariate normal but i'm really not sure.
Also, it's not a homework problem because I am too old to have homework.
Thanks for any insights/solutions.
--------------------------------------------------------
This is not an offer (or solicitation of an offer) to buy/se...{{dropped}}
______________________________________________
R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
===========================================================================================DISCLAIMER
AND CONFIDENTIALITY CAUTION:\ \ This message and ...{{dropped}}