SAS Stationarity - PACF ACF question

[adrfinance]

Hello,

I am looking at the following web page regarding stationarity:

https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=etsug&docsetTarget=etsug_...

I have two questions:

First of all, what do the shaded blue-ish lines mean for the PACF plots etc? Are these some kind of confidence intervals?

Also, in order to assess stationarity, do I need to plot the ACF and PACF and then keep as many lags as those that exceed these blue-ish lines?

[dw_sas]

Hi @adrfinance , 

You are absolutely correct regarding the light-blue shaded region in the PACF plot generated by PROC ARIMA.  It represents the approximate 95% confidence intervals about the sample partial autocorrelations.

Regarding your second question, the ACF plot is helpful in assessing the stationarity of a series.  For non-stationary series, the sample autocorrelations decay very slowly (as shown in the example you cited from the PROC ARIMA documentation).  Determining the number of augmenting lags to include in the underlying regression models used to compute the Augmented Dickey-Fuller test statistics can be a bit more involved.  The PROC ARIMA example in the link below illustrates one approach based on the results of the ESACF and SCAN options.  In particular, see the paragraph after Output 7.5.5.

https://go.documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=etsug&docsetTarget=ets... 

Another approach using PROC REG to determine the number of augmenting lags to include in the underlying regression models for the ADF tests is provided in the following SAS Global Forum paper written by Dr. Dickey:

https://support.sas.com/resources/papers/proceedings16/7080-2016.pdf 

For details about the underlying regression models used to compute the ADF test statistics, please see the following documentation link for the PROBDF function:

https://go.documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.4&docsetId=etsug&docsetTarget=ets... 

I hope this helps!

DW