# How do I interpret the ACF and PACF of differenced nominal effective exchange rate data, with the ultimate goal being to fit an ARIMA model?

Running a Dickey Fuller test, I've determined the the nominal effective exchange rate (NEER) is non-stationary. However, the difference of the NEER is stationary by the Dickey-Fuller test. The ACF of the NEER (not differenced) was very slowly decaying, providing more support that the NEER isn't stationary. So I'd like to fit an ARIMA model to the differenced NEER data.

Here is my ACF and PACF:

I am unsure of what to deduce from these images. The ACF shows a strong bar in the first lag, then another bar in the significance region at the second lag, then there's a few that show up as significant later on but its mostly insignificant. The PCAF shows a strong bar in the first lag, then a few more significant bars periodically.

Is there something I'm missing or need to take into account. Can I proceed with fitting various ARIMA models?

Thanks for the help!

• That looks like an MA(1) process to me. You'd expect about $0.05*26 = 1.3$ or so false positives in the plots, so assuming the MA(1) part is correct, you're seeing three, not too bad. I'd fit an MA(1) and check the residuals of that model just in case. – jbowman Mar 20 '18 at 0:35
• Just to clarify, the "strong bar in the first lag" in the ACF plot is actually at lag zero; it is (always) exactly 1. The PACF plot does indeed start at lag 1. – Chris Haug Mar 20 '18 at 0:49
• I wonder if the following link may prove to be useful to you: people.duke.edu/~rnau/411arim3.htm . – Isabella Ghement Mar 20 '18 at 2:13