Programming the statistical procedures from SAS

ARIMA - prewhitening procedure for studying causal relationships

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ARIMA - prewhitening procedure for studying causal relationships

Hi I wonder if anyone could check my coding of the following models. The models are used to study the causal relationships between two time series, x and y. Only one of the two time series, x, follows an MA(1) process and needs prewhitening.

The first model shown below regresses y on four input series, the concurrent value and 3 lags of the prewhitened series x:


yt = a-1 + a0 xt + a1 xt-1 + a2 xt-2 + a3 xt-3 + et

I follow the prewhitening example found in the SAS documentation to build the following lines:

proc arima data=in;
identify var=x;
estimate q=1;
identify var=y crosscorr=x;
estimate input=(x x(1) x(2) x(3))
run;
quit;

My concern is that in the SAS documentation, it suggests that the above procedures will filter both x and y by the MA(1) model. As I need to regress the unfiltered y series on the prewhitened x series (concurrent plus 3 lags), I am not sure if this requirement corresponds to the 2nd estimate statement.

To complete the study on causal relationship, I also need to swap the input and response series as follows:

xt = b-1 + b0 yt + b1 yt-1 + b2 yt-2 + b3 yt-3 + ut

I wonder if the following codes are correct:

proc arima data=in;
identify var=x;
estimate q=1;
identify var=x crosscorr=y;
estimate input=(y y(1) y(2) y(3))
run;
quit;

Thank you
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