I have so far concluded that the ACF and PACF show a potential ARIMA (1, 2, 1). Are there any other possibilities of ARIMA models that could also fit this data?
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$\begingroup$ Why would you need both "1" terms there? $\endgroup$– Glen_bCommented Dec 10, 2015 at 15:16
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1$\begingroup$ Second-order differencing is not common in economics (or perhaps in general). What kind of process do you have? Perhaps second-order differencing does not make sense when viewed from the subject-matter perspective. $\endgroup$– Richard HardyCommented Dec 10, 2015 at 15:21
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$\begingroup$ Why can you not have both terms equal to 1, if both show significance at lag 1? $\endgroup$– Gabriella101Commented Dec 10, 2015 at 15:24
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$\begingroup$ If you answer a comment by some user, use @username (e.g. @RichardHardy) to make sure the addressee is notified about your message. $\endgroup$– Richard HardyCommented Dec 10, 2015 at 18:19
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When deciding between an AR model and an MA model one looks for dominance between the ACF and the PACF:
If the ACF dominates then choose an AR model with the order dictated by the PACF.
If the PACF dominates then choose an MA model with the order dictated by the ACF.
If there is ambiguity then there might be a combined model BUT I would proceed slowly by selecting one and then reviewing the model residuals to suggest further augmentation.
Recall that the above advice is a rule of thumb and is probably worthless when you have any of the following:
outliers/pulses/step shifts/local time trends
parameters that are changing over time
a model error variance that is non-constant.
