0
$\begingroup$

While working with a data on sp500 I have encountered one problem concerning the interpretation of ac and pac graphs. The problem is that none of them shows a significant lag outside of confidence band. I do not know how to choose p and q in this case in order to build my ARIMA model. Any help would be highly appreciated. I am also attaching the graphs.

*ac d.lnclose*

*pac d.lnclose*

$\endgroup$
1
  • $\begingroup$ If all ACF and PACF values are within the confidence bounds, then what about ARIMA(0,0,0)? (PACF value #2 seems to be borderline significant, though.) $\endgroup$ Oct 17, 2017 at 16:51

1 Answer 1

4
$\begingroup$

These functions inform us that there is no significant autoregressive component in your data, so p = 0.

You don't need to take differences of master data as well since you do not see declining autogression from lag 1 to 40 (referring to your charts), existence of which would be an indication of long memory, artifact of having not stationary (trendy data). So, d = 0.

Given that you cannot expect that your residuals contain any autoregressive dependency in the absence of any significant dependencies to model (and to produce residuals), the q component seems to be zero as well. So, q = 0.

ARIMA(0,0,0)

It looks like a good approximation of ARIMA parameters to your data.

Update: I just saw @Richard Hardy's comment while I was typing, so we came in simultaneously.

$\endgroup$
3
  • $\begingroup$ Thank you for the explanation. Differencing of the variable was not my choice but rather a demand of a professor. $\endgroup$ Oct 17, 2017 at 16:56
  • $\begingroup$ I understand you had already differenced raw SP500 prior to using ac/pac. So I mean you need no higher order differencing. $\endgroup$ Oct 17, 2017 at 16:57
  • $\begingroup$ Differencing makes sense from a theoretical point of view. Stock prices should not tend towards an overall mean as an ARIMA(0,0,0) process. To a first approximation, the current price should include all currently known information, so only increments over today's price should be ARMA(0,0). That is, you should have a random walk, which is an ARIMA(0,1,0) process. The next step in modeling would be to model variance using an ARCH or GARCH process. $\endgroup$ Oct 17, 2017 at 20:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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