When identifying a transfer function by the prewhitening method, the
input series x and response series y must be jointly stationary.  If
necessary, they must be made stationary by appropriate differencing.

In lecture, the x and y series in the gas furnace example did not
require any differencing.  If differencing is needed, the type of
differencing is specified in the var= and crosscor= parts of the
identify statements.

To illustrate this, we give three proc arima steps.  The first is for
the case when no differencing is needed.  (This is just the proc arima
step from lecture after deleting the alternative transfer function.)
The second proc arima step illustrates the case where both x and y
require differencing once at lag 1.  The third step illustrates the
case where both x and y require differencing twice at lag 1.

/* No differencing needed. */

proc arima data=gas;
i var=x;
e p=3 method=ml;
i var=y crosscor=x;
e input=(3$(1,2)/(1)x) method=ml;
e p=2 input=(3$(1,2)/(1)x) method=ml;
quit;

/* Both x and y require differencing once. */

proc arima data=gas;
i var=x(1);
e p=3 method=ml;
i var=y(1) crosscor=x(1);
e input=(3$(1,2)/(1)x) method=ml;
e p=2 input=(3$(1,2)/(1)x) method=ml;
quit;

/* Both x and y require differencing twice. */

proc arima data=gas;
i var=x(1,1);
e p=3 method=ml;
i var=y(1,1) crosscor=x(1,1);
e input=(3$(1,2)/(1)x) method=ml;
e p=2 input=(3$(1,2)/(1)x) method=ml;
quit;