## PRODUCT Function

**multiplies matrices of polynomials**
**PRODUCT(** *a*, *b*<, dim>**)**

The inputs to the PRODUCT function are as follows:
*a*
- is an
*m* ×(*ns*) numeric matrix.
The first *m* ×*n* submatrix contains the constant
terms of the polynomials, the second *m* ×*n*
submatrix contains the first order terms, and so on.

*b*
- is an
*n* ×(*pt*) matrix.
The first *n* ×*p* submatrix contains the constant
terms of the polynomials, the second *n* ×*p*
submatrix contains the first order terms, and so on.

*dim*
- is a 1 ×1 matrix, with value
*p*>0.
The value of this matrix is used to set *p* above.
If omitted, the value of *p* is set to 1.

The PRODUCT function multiplies matrices of polynomials.
The value returned is the *m* ×(*p*(*s*+*t*-1))
matrix of the polynomial products.
The first *m* ×*p* submatrix contains the
constant terms, the second *m* ×*p* submatrix
contains the first order terms, and so on.

**Note:** The PRODUCT function can be used
to multiply the matrix operators employed in
a multivariate time-series model of the form

where , , , and
are matrix polynomial operators whose
first matrix coefficients are identity matrices.
Often and represent seasonal components
that are isolated in the modeling process but multiplied with the
other operators when forming predictors or estimating parameters.
The RATIO function is often employed
in a time series context as well.
For example, the statement

r=product({1 2 3 4,
5 6 7 8},
{1 2 3,
4 5 6}, 1);

produces the result
R 2 rows 4 cols (numeric)
9 31 41 33
29 79 105 69

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.