I'm reading Tsay's time series book. The ACFs and PACFs looks like this: ACFs and PACFs

My question is: how to specify an ARMA model (p=?, q=?) based on the above figure? The author did give some ideas, but I'm totally confused. The first eight lags of PACFs are significant. This implies that q (order of MA part) >0. Why? The PACFs do not follow a simple exponentially decaying pattern. This means p (order of AR part) >1. Why? Somehow I think AR(8) would be a good choice. Is it reasonable?

Explanation in the book

Is there any general rule about how to specify an ARMA model? Thanks!

  • $\begingroup$ Personally I'd have started with an AR(3). The remaining PACF lags are all pretty small and having a few outside a 95% interval is no big news (yes, there's more than you'd expect, but that doesn't necessarily mean you're better off with them in a model). $\endgroup$ – Glen_b May 8 '17 at 5:38

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