0
$\begingroup$

I have yearly data. When I do a Dickey-Fuller test it gives me insignificant results, indicating that the series are non-stationary. After differencing them the DFT tells me they are now significant and stationary.

When using an ACF/PACF plot on the original series it is obvious that an AR(1) process should be used.

When plotting ACF/PACF for the first difference I can't make that same inference again because there is no significant spike in the ACF.

ACF

PACF

$\endgroup$

1 Answer 1

0
$\begingroup$

There is nothing conflicting here. Differencing a unit root process removes the unit root. If the original process is AR(1) with a unit root, $y_t=y_{t-1}+\varepsilon_t$, the differenced process is just white noise, $\Delta y_t=\varepsilon_t$. This is what you see in the ACF and PACF for the differenced data.

$\endgroup$
4
  • $\begingroup$ Based on that you would conclude that you would use an AR(1) process? $\endgroup$
    – Narog
    May 14 at 20:03
  • $\begingroup$ @Narog, why the question? You write: When using an ACF/PACF plot on the original series it is obvious that an AR(1) process should be used. If it is obvious, then it is obvious, or?.. $\endgroup$ May 14 at 20:06
  • $\begingroup$ shouldn't you look at the ACF/PACF of the stationary data? The non-stationary looks like an AR1 but the stationary more like a MA1 or am I incorrect assuming this. $\endgroup$
    – Narog
    May 15 at 12:06
  • $\begingroup$ @Narog, all the bars are inside the confidence bounds. That is a signature of white noise. Where do you see any signs of MA(1)? (Note: ACF(0) is always 1, regardless of the data generating process.) $\endgroup$ May 15 at 12:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.