ACF and PACF plots - MA, AR, ARIMA, or neither?

[Alexandra Voight]

I differenced the variable (univariate model) in question because it was not stationary. I ran the dickey-fuller unit root test to check for stationarity, and it looks like the differenced version is stationary. However, when I make the acf and pacf plots to determine the model, I get these bizarre results that I do not know how to interpret. Could someone please help me understand? Thanks

[Oscar Ozfidan]

ACF and PACF are diagnostic tools to highlight which lags appear to have some useful predictive power based on correlation. You did not provide information on the period of data (monthly, quarterly, weekly, etc). Looks like though the 9th and the 16th lags are sticking out. These would change though when you add the lags. So, I recommend you start with AR and MA terms for the 9th lag (first AR(9) then MA(9) and watch happens to the plots and Akaike criterion. The goal is to optimize Akaike criterion. It would not be unusual to low order ar ma terms to be significant when you incorporate the 9th lag. This is basically trial and error. I use some other software that has built in automated process to check all possible combinations and dont use stata but that is how you can approach the problem. Then You need to pay particular attention to seasonal terms (e.g. 12th, 24th lags in monthly data, 4th, 8th in quarterly etc) the interpretation will strictly depend on what the period is. But basically all you can say is these are the lags that appear significant and that is why included in the model. Why are they significant will depend on the context. Also, keep in mind just because a lag is significant does not mean it truly is. You will have a significant lag 5 out of 100 terms when it is not.