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Suppose I fit an AR(2) model to a dataset and get the diagnostics. If the Ljung-Box Statistic is significant for all lags for a time series model what is the interpretation of that? Does that mean that the model is not a good fit? Other than this, the ACF of the residuals indicate that they are stationary and normal.

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  • $\begingroup$ It is the case (no white noise/iid). Details here. How did you use ACF to decide that it is normal? $\endgroup$ – Metrics Apr 18 '13 at 4:56
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Are you testing the residuals of the AR(2)? In that case, H0 of the Ljung-Box test is independence, and independence of the residuals is assumed when you fit an AR(p), so that is a good thing. If the Box.test is rejected, your residuals are serially correlated and the order of your model might be wrong, and you should try a different lag length.

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