Need help interpreting ACF and PACF plots for ARIMA

Question

Based on my understanding, we can identify the order of an AR process based on where there is a drop in the PACF and for the MA process it is when there is a drop in the ACF.

Both these two graphs are really peculiar to me. It seems that there is no drop; the ACF is decaying exponentially while the PACF seems to have an alternating pattern that is also decaying exponentially. In such a scenario, how do we determine the appropriate orders of an ARIMA model?

Answer 1

Your reasoning is right for exclusive AR or MA process. But in this case, it's seems to be an ARMA Process with $p$ and $q$ coefficients. In this case the order can be quite challenging, but always start with ARMA(1,1), then ARMA(2,1) and ARMA(1,2). Usually the ARMA(1,1) outperforms the other two. To choose you need an information criterion (BIC or AIC). This is called a search for an optimal lag length.