Distinguish an ARMA and an ARIMA model graphically I'm currently analyzing some time series data and I need to know how to distinguish an ARMA model from an ARIMA model just by looking at the auto-correlation function and partial auto-correlation function of a seasonal series. 
 A: It is not easy to distinguish an ARMA model from an ARIMA model graphically.  The problem is that the stationary ARMA form can be made arbitrarily close to the ARIMA form by setting one of the roots of the auto-regressive characteristic polynomial arbitrarily close to one.  Trying to distinguish between these models is equivalent to trying to determine whether there is a unit root in the auto-regressive characteristic polynomial.  This usually requires formal modelling and testing, and it is not something that is easy to do on a purely graphical basis.
A: Given that are no Pulses, Level Shifts, Seasonal Pulses, Local Time Trends AND the ultimate ARIMA parameters and model error variance are constant over time AND that you have suitably (not over) differenced the series to obtain stationarity THEN: compare the acf and the pacf for dominance. Examine the dominant one and if it has a decaying structure conclude that the model has an AR component if the dominant one was the acf and alternatively an MA structure if the dominant one was the pacf. The order of the AR or MA structure is based upon the number of significant coeffficients in the subordinate. This might be of some help http://www.autobox.com/cms/index.php/blog/entry/build-or-make-your-own-arima-forecasting-model . The idea is that ARIMA model identification sometimes(often) requires a sequence of model identification/estimation/diagnostic checking in order to detect the underlying signal (ARIMA model). Think of the first pass as the residuals from a mean model ( the first tentative model) and you can understand that there is no such thing as "an identification phase" just a sequence of model revision phases.
