# [R] pacf

Martin Maechler maechler at stat.math.ethz.ch
Sat Apr 28 21:47:58 CEST 2007

```>>>>> "tom" == tom soyer <tom.soyer at gmail.com>
>>>>>     on Sat, 28 Apr 2007 08:15:39 -0500 writes:

tom> I wanted to understand exactly how acf and pacf works,
tom> so I tried to calculate ac and pac manually. For ac, I
tom> used the standard acf formula: acf(k) =
tom> sum(X(t)-Xbar)(X(t-k)-Xbar))/sum(X(t)-Xbar)^2. But for
tom> pac, I could not figure out how to calculate it by
tom> hand. I understand that in both R and EVIEWS, it is
tom> done using the Durbin-Levinson algorithm by the
tom> computer.  However, I don't understand exactly how the
tom> algorithm works just by looking at the algorithm. Does
tom> anyone know if there is a short cut to calculate pac by
tom> hand (or in a spreadsheet), or is it too complex of a
tom> procedure that a computer is absolutely necessary? It
tom> seems that there should be a natural relationship
tom> between ac and pac so that once ac is calculated, pac
tom> can be easily calculated based on ac.

"easily", yes, by the Durbin-Levinson algorithm  ;-)

(is this a homework problem?)

Martin Maechler, ETH Zurich

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