My email does not seem to receive any attention on R-help, so I
forward it on R-devel if someone has already faced the "problem".
Thanks in advance
Christophe
Début du message réexpédié :
> De : Christophe Dutang <duta...@gmail.com>
> Date : 13 novembre 2009 23:30:14 HNEC
> À : r-h...@r-project.org
> Objet : AR(2) modelling
>
Hi useRs,
I'm trying to fit a basic AR(2) model with the 'ar' function. And when
I try to check the value of the coefficients, I could not find the
same value as the 'ar' function.
Here is my example:
myserie <- c(212, 205, 210, 213, 217, 222, 216, 218, 220, 212, 215, 236)
#plot(myserie, type="l")
myserieminus0 <- tail(myserie, -2)
myserieminus1 <- tail(head(myserie, -1), -1)
myserieminus2 <- head(myserie, -2)
###Yule Walker equations
r1 <- cor(myserieminus0, myserieminus1)
r2 <- cor(myserieminus0, myserieminus2)
#method 1
phihat1 <- r1*(1-r2)/(1-r1^2)
phihat2 <- (r2-r1^2)/(1-r1^2)
#method 2
bigR <- cbind(c(1, r1), c(r1, 1))
smallr <- c(r1, r2)
ressolve <- solve(bigR, smallr)
resaryw <- ar(myserie, method="yule-walker", order.max=2, aic=FALSE)
cat("\t\tmanual YW 1\t\tmanual YW 2\t\tar YW\n")
cat("first coef", phihat1,"\t", ressolve[1],"\t\t", resaryw$ar[1], "\n")
cat("first coef", phihat2,"\t", ressolve[2],"\t", resaryw$ar[2], "\n\n")
> manual YW 1 manual YW 2 ar YW
> first coef 0.2941808 0.2941808 0.1869641
> first coef -0.1316839 -0.1316839 -0.1038001
I do not understand why the "yule-walker" does not solve exactly the
Yule-Walker equations. A reference can be found here
http://www-stat.wharton.upenn.edu/~steele/Courses/956/ResourceDetails/YWSourceFiles/YW-Eshel.pdf
.
In the R source code (<src>/src/library/stats/R), the file ar.R
contains the ar.yw.default function implements the function. For
univariate case (line 130), r_eureka function is used, which seems to
be implemented in the eureka.f function.
subroutine eureka (lr,r,g,f,var,a)
c
c solves Toeplitz matrix equation toep(r)f=g(1+.)
c by Levinson's algorithm
c a is a workspace of size lr, the number
c of equations
c
is supposed to implement the Yule-Walker equations...
Any help is welcome.
Just to be sure, I can do something I try to reconcile the ordinary
least square methods. And it works!
Christophe
PS : OLS code
###Ordinary Least Square
reslm <- lm(myserieminus0 ~ myserieminus1 + myserieminus2)
#summary(reslm)
coef1ols <- reslm$coefficients["myserieminus1"]
coef2ols <- reslm$coefficients["myserieminus2"]
resarols <- ar(myserie, method="ols", order.max=2, aic=FALSE)
cat("\t\tmanual ols\t\tar ols\n")
cat("first coef", coef1ols,"\t", resarols$ar[1], "\n")
cat("first coef", coef2ols,"\t", resarols$ar[2], "\n\n")
--
Christophe Dutang
Ph.D. student at ISFA, Lyon, France
website: http://dutangc.free.fr
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