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.
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.