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# Proc ARIMA notation for the input series

Hi I was wondering if anyone could help me in understanding the ARIMA notation for the input series. Basically i have a response time series y and I have x1 and x2 as my inputs. I did the prewhitening before calculating the crosscorrelation. The prewhitening filter for x1 is ARIMA(1,1,2) and for x2 is ARIMA(0,1,2). And based on the crosscorrelation, I'd like to include lag2 for x1 and lag3 for x2, but I'm not sure how to correctly code it in the "estimate" statement such that the previous whitening filter is taken into account. So far, i have:
proc arima data=fit
identify var=x1(1); estimate p=1 q=2 noint;
identify var=x2(1); estimate q=2 noint;
identify var=y crosscorr=(x1(1) x2(1));
estimate input=(??x1 ??x2) noint;
run;quit;
Thank you.
SAS Employee
Posts: 416

## Re: Proc ARIMA notation for the input series

Hello -
According to documentation of the CROSSCORR option: "Each variable name can be followed by a list of differencing lags in parentheses, the same as for the VAR= specification. If differencing is specified for a variable in the CROSSCORR= list, the differenced series is cross-correlated with the VAR= option series, and the differenced series is used when the ESTIMATE statement INPUT= option refers to the variable."
So this might be what you are looking for:
proc arima data=test;
identify var=x1(1);
estimate p=1 q=2 noint;
identify var=x2(1);
estimate q=2 noint;
identify var=y crosscorr=(x1(2) x2(3));
estimate input=(x1 x2) noint;
run;quit;
Regards,
Udo
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