A seasonal autoregressive moving-average model, denoted 
, is an autoregressive
moving-average model with additional autoregressive and moving-average terms
at integer multiples of a seasonal period 
. Using the shift operator 
defined by 
, a centered model can be written
 |
where 
and 
are respectively the nonseasonal autoregressive and moving-average
polynomials, 
and 
are their seasonal counterparts, and the 
are innovations. The
orders 
and 
give the degrees of 
and 
, while 
and 
give the degrees of 
and 
. When 
, the model reduces to an autoregressive
moving-average model.
A seasonal autoregressive moving-average process can be represented in the Wolfram Language using SARMAProcess[a,
b, 
s, alpha, beta
, v].
