> to be no means for testing whether it should be AR1, AR2, ... ARN..
How about partial autocorrelation?
If the timeseries is (pure) AR[p] or MA[q] the autocorrelation (ACF) and
partial autocorrelation (PACF) can help you to specify the order of p or q.
The timeseries is MA[q] if for the ACF holds: $\rho_{q} \neq 0$ and
$\rho_{\tau} = 0$ for $\tau > q$.
The timeseries is AR[p] if for the PACF holds: $\pi_{p} \neq 0$ and
$\pi_{\tau} = 0$ for $\tau > p$.
You can calculate the PACF with the Levinson-Durbin recursion. For ARMA[p,q]
models you can use a table of vectorcorrelations.
Sorry for my english.
Alexander
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