Simone Giannerini wrote: > Dear Paul, > > there is no mention to the pacf in the multivariate setting in the book > you suggested.
My apologies, I should have looked more carefully and realized the pacf discussion in Granger and Newbold is all univariate. > As I mentioned in private I suspect that pacf() in the multivariate case > computes the > partial autoregression matrix (in the terminology of Reinsel) rather > than the partial autocorrelation matrix It looks like pacf() uses the calculation in stats:::ar.yw.default , so roughly sounds consistent with what you say. I do think parts of this code pre-date Reisel's book, so inconsistency with his book would probably be imperfect foresight. BTW, I think bug reports with suggested fixes are usually more useful. And, at the very least, it seems the references in the documentation could be improved. Paul Gilbert > as the two coincide in the univariate case but are different in the > multivariate case as stated explicitly > in Reisel (Sec. 3.3). > This would explain the coefficients well above 1 (in modulus) in the > example I have given. > To support my statement you can fit A VAR model to the data and compare > the coefficients with the results > from pacf(): > > set.seed(10) > x <- rnorm(1000,sd=10000) > y <- rnorm(1000,sd=1) > > library(vars); > mod1 <- VAR(ts(cbind(x,y)),p=4,type="none"); # fit a VAR (OLS) > > ## Have a look at estimated coefficients > >> noquote(formatC(mod1$varresult$x$coefficients,format="f")) > ## Edited by me, compare with the first column of the results below from > the pacf (pacf(....)$acf[,1,]) > x.l1 x.l2 x.l3 x.l4 > 0.047 0.013 0.004 0.014 > y.l1 y.l2 y.l3 y.l4 > 374.117 72.758 -526.452 126.610 >> noquote(formatC(mod1$varresult$y$coefficients,format="f")) > ## Edited by me, compare with the second column of the results below > from the pacf (pacf(....)$acf[,2,]) > x.l1 x.l2 x.l3 x.l4 > 0.000 -0.000 0.000 0.000 > y.l1 y.l2 y.l3 y.l4 > -0.046 -0.025 -0.033 -0.020 > > pacf(ts(cbind(x,y)),plot=FALSE,lag.max=4) > > Partial autocorrelations of series 'ts(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) > > , , 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) > > As you can see the coefficients fairly agree. > I might file a bug report in some days unless someone will prove me > wrong before. > > Regards, > > Simone > > > > On 11/09/2007, *Paul Gilbert* <[EMAIL PROTECTED] > <mailto:[EMAIL PROTECTED]>> wrote: > > I think the reference for pacf is > > @BOOK{GraNew77, > author = {Granger, C. W. J. and Newbold, Paul}, > title = {Forecasting Economic Time Series}, > publisher = {Academic Press}, > year = 1977 > } > > It certainly would not be Reisel's book, as parts of the code predate > that by many years. > > Paul Gilbert > > Simone Giannerini wrote: > > 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)" > > ==================================================================================== > > La version française suit le texte anglais. > > > ------------------------------------------------------------------------------------ > > > This email may contain privileged and/or confidential information, > and the Bank of > Canada does not waive any related rights. Any distribution, use, or > copying of this > email or the information it contains by other than the intended > recipient is > unauthorized. 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