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Now, here are the rules for determining p and q from the plots of autocorrelations and partial
autocorrelations:
i. If the ACF plot “cuts off sharply” at lag k (i.e., if the autocorrelation is significantly
different from zero at lag k and extremely low in significance at the next higher lag and
the ones that follow), while there is a more gradual “decay” in the PACF plot (i.e. if
the dropoff in significance beyond lag k is more gradual), then set q=k and p=0. This
is a so-called “MA(q) signature.”
ii. On the other hand, if the PACF plot cuts off sharply at lag k while there is a more
gradual decay in the ACF plot, then set p=k and q=0. This is a so-called “AR(p)
signature.”
iii. If there is a single spike at lag 1 in both the ACF and PACF plots, then set p=1 and q=0
if it is positive (this is an AR(1) signature), and set p=0 and q=1 if it is negative (this is
an MA(1) signature).
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