Sample Inverse Partial Autocorrelation Function

[sasalex2024]

Dear SAS Community,

Some time-series textbooks mention the usefulness of the inverse partial autocorrelation function (IPACF) in identifying the type of ARMA model for a series. Personally, I try not to rely solely on automatic model identification procedures, even though they are extremely helpful, and I prefer to double-check them with traditional methods. These methods can be especially valuable when the best model turns out to be a constrained ARMA model (with some parameters being restricted to zero).

It is my understanding that the SAS proc arima procedure does not generate the IPACF. Is there a way to obtain it in SAS?

I would greatly appreciate your insights on this.

[SASCom1]

PROC ARIMA produces ACF, IACF, PACF plots, but no IPACF. I have not seen discussions on IPACF, can you provide references for the text book(s) you mentioned with information on IPACF? 

[sasalex2024]

Hello SAScom1,

Thank you for your reply. Hipel and McLeod (1994) uses IPACF extensively. Please see Chapter 5 (p. 184), for example, available here: https://www.eng.uwaterloo.ca/~kwhipel/Time%20Series%20Book.htm 

Full reference: 

Hipel, Keith W. and Ian McLeod. “Time series modelling of water resources and environmental systems.” (1994).

[SASCom1]

Thanks for providing the reference. From your reference, chapter 5, p.184, it discusses how you can obtain estimate for the IPACF, in the second paragraph right after equation 5.3.4. You may follow the discussed methods there to obtain the estimated IPACF, for example, for the first method discussed, 'replace the rho_i,k by sample IACF r_i,k, and solve the inverse Yule-Walker equations for the estimated theta_k,k', you only need to have the sample IACF r_i,k , which you can obtain in PROC ARIMA, you can then solve the inverse Yule-Walker equations (5.3.4) to get the estimated theta_k,k. 

I hope this helps.

[sasalex2024]

Thank you!