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].
