This is a good question. If your second transfer function spec did not have a denominator polynomial with unit root, you could have easily specified this model by including an extra copy of your I variable, say copy_I, in your input data set. As it happens, the denominator polynomials in ARIMA cannot be "unstable". One way to get around this and specify a model that is reasonably close to your model is as follows (this still involves making a copy of the I variable):
Note that after multiplying your model equation by (1-B), one gets the following:
I have renamed your I variable as X. For simplicity, let us assume that your noise process N_t is a simple white noise. Then (1-B) N_t is an MA(1) process with MA parameter equal to 1 (which is noninvertible). In ARIMA you can specify a model close to this rearranged model where the noise is invertible MA(1). You could do this as follows:
Suppose your input data set is TEST.
Step1. Create a copy of variable X:
copy_X = X;
Step 2: Specify the model:
proc arima data=test; i var=y(1) crosscorr=(X copy_X(1)) noprint; e q=1 input=(/(1) copy_X X) noint method=ml; quit;
This will give you a specification reasonably close to what you want. If in fact, the true noise process is non-invertible MA(1), your estimated MA parameter will be close to it.
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