BookmarkSubscribeRSS Feed
Obsidian | Level 7

Hello, I would l would like to know how one could specify the following compounded transfer function. This gives a compounded effect of abrupt spike and decay and settles in a new mean.arima_transfer_eq.PNG


This can be visualized as follows. I can easily code the first part of the equation, the question is how to compound both with same intervention variable. Thanks in advance



SAS Employee

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:

(1-B) y_t = (omega_01/(1-delta B)) (1-B) X_t + omega_02 X_t + (1-B) N_t.

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:

   data test;

       set test;

       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;


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.


Hope this works OK for you.



Registration is open! SAS is returning to Vegas for an AI and analytics experience like no other! Whether you're an executive, manager, end user or SAS partner, SAS Innovate is designed for everyone on your team. Register for just $495 by 12/31/2023.

If you are interested in speaking, there is still time to submit a session idea. More details are posted on the website. 

Register now!

Multiple Linear Regression in SAS

Learn how to run multiple linear regression models with and without interactions, presented by SAS user Alex Chaplin.

Find more tutorials on the SAS Users YouTube channel.

Discussion stats
  • 1 reply
  • 1 like
  • 2 in conversation