[R] pacf

Prof Brian D Ripley ripley at stats.ox.ac.uk
Tue Jun 20 16:39:53 CEST 2000

On Tue, 20 Jun 2000, Christian Kleiber wrote:

> Dear list,
> according to the documentation of acf{ts}
> "the partial correlation coefficient is estimated by fitting
> autoregressive models of successively higher orders up to lag.max. "
> However, R seems to return the Yule-Walker estimates of the PACF by
> default. 

R provides four methods to `Fit Autoregressive Models to Time   
Series' in function ar(), and the default there is indeed Yule-Walker, so
this seems self-consistent.

> You can check this using c(1:10) as the series: the YW
> estimates are 0.7000000 and  -0.1527035 for lags 1 and 2 . If the PACF
> really was estimated from running autoregressions, the first coefficient
> should be 1 and one would expect an error message for higher-order
> coefficients (due to singularity of the regression matrix). pacf() or
> acf (..., type="partial", ...), however, return 0.7000000 and
> -0.1527035.

It does not say `running autoregressions', and I believe it to be standard
in the time-series field to fit autoregressive models *by Yule-Walker* to
estimate pacfs.  Indeed, in the first two books I have just looked in, that
is the definition of the sample PACF (in the univariate case).  So I don't
think these are `the Yule-Walker estimates of the PACF' but the `sample

I assume by `running autoregressions' you mean what ar.ols does: if that is
what you want that is provided too.  But it is not the only nor even the
usual meaning of `fitting' an AR(p) model to time-series data, especially
assuming stationarity (as the definitions of acf and pacf do).

I am a bit of a loss as to what your point was.  Are you really suggesting
that what R (and S) does is not absolutely standard using standard
terminology?  If so your bookshelf must be a disjoint set from mine.

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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