Reading ACF and PACF to name the model

Question

For a stationary series you examine two plots. The sample ACF decays roughly geometrically toward zero across lags. The sample PACF is clearly significant at lag 1 and then drops inside the bands for all higher lags.

Which model does this pattern indicate?

Accepted Answer

The two diagnostic plots read like a lookup table: - AR(p): ACF tails off (decays gradually), PACF cuts off sharply after lag p. - MA(q): ACF cuts off sharply after lag q, PACF tails off. - ARMA: both tail off gradually. Here the ACF tails off (geometric decay) and the PACF cuts off after lag 1. Matching the first rule with p = 1 gives an AR(1) model. The intuition: the partial autocorrelation strips out the indirect correlation carried through intermediate lags. For an AR(1), once you account for lag 1 there is no direct link at lag 2 or beyond, so the PACF snaps to zero after the first spik…

Reading ACF and PACF to name the model

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