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I know that when trying to determine if you have an AR(p) or MA(q) process, you look at the PACF and if it drops off significantly at a lag p, then you can say it's an AR(p), but if it's geometrically decaying and the ACF is significant till a lag, then it's likely an MA(q). But what if neither plot obviously shows these patterns?

For instance (looking at the attached pic), neither my ACF (of the twice differenced series) nor PACF (of once differenced & transformed series) are showing decay. Also neither shows a sudden drop off at a specific lag. If I had to guess I would propose an ARIMA(1,1,0), but again I'm really not sure.

enter image description here

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Well despite the differencing this might indicate data that is still non-stationary or has seasonal non-stationarity which is the classic answer to why no decay is occurring. I have data that I could never get to be stationary. Also you may need to consider seasonal differencing or seasonal AR and MA terms (they tend to spike at 12 lags for monthly data).

What does your ADF test say after the two differencing.

Note that with mixed data trying to identify the correct model is rough, the ACF and PACF will not easily identify your model. That is the classical approaches shown in text do not easily work with them according to some experts.

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