R help - Apr 2007 - pacf

Hi,

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

-- 
Tom

	[[alternative HTML version deleted]]

>>>>> "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