[R] pacf, round two

Prof Brian D Ripley ripley at stats.ox.ac.uk
Wed Jun 21 20:03:57 CEST 2000

On Wed, 21 Jun 2000, Christian Kleiber wrote:

> A leading text, Brockwell and Davis 1991 (I assume our bookshelves are not
> disjoint?), defines the theoretical PACF in two different ways (YW, OLS) and
> shows that both definitions are equivalent. Later, the sample PACF is solely
> defined via YW. 

Exactly, on page 102. My copy says nothing about OLS on pages 98-102, which
is what the index points to for the definition of the PACF. This was the
first book I picked up.

I don't see how the theoretical PACF can be defined by methods of
estimation.  Partial correlation coefficients have nothing to do with OLS.

> In the S-PLUS Help on acf() one finds
> "... For the partial autocorrelation function, the Levinson-Durbin recursion is
> used to fit AR(p) models to x successively for p = 1, ..., lag.max, and from
> the AR-coefficients the partial autocorrelation function values are derived."
> This is unambiguous. I feel R users would be better off if the algorithm

No, it isn't. To what is the Levinson-Durbin recursion recursion applied?
There are lots of the correlation matrix estimates to start it.

BTW, I did not write that page but I feel that only people who are careless
would be misled.

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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