Dear all,

I found the following behaviour with pacf() in the multivariate case,

set.seed(10)
x <- rnorm(1000,sd=10000)
y <- rnorm(1000,sd=1)
pacf(ts(cbind(x,y)),plot=FALSE,lag.max=10)

Partial autocorrelations of series 'cbind(x, y)', by lag

, , x

 x              y
    0.047 (  1)    0.000 ( -1)
    0.011 (  2)    0.000 ( -2)
    0.005 (  3)    0.000 ( -3)
    0.013 (  4)    0.000 ( -4)
    0.050 (  5)    0.000 ( -5)
    0.034 (  6)    0.000 ( -6)
    0.026 (  7)    0.000 ( -7)
   -0.029 (  8)    0.000 ( -8)
   -0.010 (  9)    0.000 ( -9)
   -0.013 ( 10)    0.000 (-10)

, , y

 x              y
  374.052 (  1)   -0.045 (  1)
   66.717 (  2)   -0.024 (  2)
 -535.810 (  3)   -0.031 (  3)
  120.802 (  4)   -0.020 (  4)
  142.824 (  5)    0.004 (  5)
 -211.711 (  6)   -0.010 (  6)
  201.856 (  7)    0.058 (  7)
  286.079 (  8)   -0.035 (  8)
 -134.057 (  9)    0.032 (  9)
  -18.200 ( 10)    0.019 ( 10)

Since there are multiple ways of defining the pacf for multivariate time
series
(see e.g. G.C. Reinsel, Elements of multivariate time series analysis, II
edition, Springer, section 3.3) and given that
in ?pacf there is no reference to articles or books regarding its
computation
I do not know whether this behaviour is expected or it is a bug instead.
In the first case could you provide a reference for it? In the second case I
might file a bug report.
Thank you for the great work you are doing for the scientific community.

kind regards,

Simone Giannerini

WINDOWS

platform       i386-pc-mingw32
arch           i386
os             mingw32
system         i386, mingw32
status
major          2
minor          5.1
year           2007
month          06
day            27
svn rev        42083
language       R
version.string R version 2.5.1 (2007-06-27)

LINUX

> R.Version()
$platform
[1] "x86_64-unknown-linux-gnu"

$arch
[1] "x86_64"

$os
[1] "linux-gnu"

$system
[1] "x86_64, linux-gnu"

$status
[1] ""

$major
[1] "2"

$minor
[1] "5.1"

$year
[1] "2007"

$month
[1] "06"

$day
[1] "27"

$`svn rev`
[1] "42083"

$language
[1] "R"

$version.string
[1] "R version 2.5.1 (2007-06-27)"
-- 
______________________________________________________

Simone Giannerini
Dipartimento di Scienze Statistiche "Paolo Fortunati"
Universita' di Bologna
Via delle belle arti 41 - 40126  Bologna,  ITALY
Tel: +39 051 2098262  Fax: +39 051 232153
______________________________________________________

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