 |
BUILT-IN MATHEMATICA SYMBOL
SARIMAProcess
SARIMAProcess[{a1, ..., ap}, d, {b1, ..., bq}, {s, {
1, ..., m}, 
, {
1, ..., r}}, v]
represents a seasonal integrated autoregressive moving-average process with ARIMA coefficients 
, d, and 
; seasonal order s; seasonal ARIMA coefficients 
, , and 
; seasonal integration order ; and normal white noise with variance v.
SARIMAProcess[{a1, ..., ap}, d, {b1, ..., bq}, {s, {1, ..., m}, , {1, ..., r}}, 
]
represents a vector SARIMA process with coefficient matrices 
, 
, 
, and 
and covariance matrix .
SARIMAProcess[{a1, ...}, {d1, ...}, {b1, ...}, {{s1, ...}, {1, ...}, {1, ...}, {1, ...}}, ]
represents a vector SARIMA process with multiple integration orders 
, seasonal orders 
, and seasonal integration orders 
.
Details
- SARIMAProcess is a discrete-time and continuous-state random process.
- The SARIMA process is effectively the composition of an ARIMA process and a seasonal version of an ARIMA process.
- The SARIMA process is described by the difference equations
, 
, where 
is the state output, 
is white noise input, and 
is the shift operator. - The scalar SARIMA process has transfer function
, where 
, 
. - The vector SARIMA process has transfer matrix
, where 
, 
, and where 
is the 
×
identity matrix. - A scalar SARIMA process should have real coefficients
, 
, 
, and 
, positive integer seasonality order s, non-negative integer integration orders d and , and a positive variance v. - An
-dimensional vector SARIMA process should have real coefficient matrices 
, 
, 
, and 
of dimensions 
×
; positive integer seasonality orders 
or s; non-negative integer integration orders 
or d, as well as 
or ; and symmetric positive definite covariance matrix of dimension 
×
. - SARIMAProcess can be used with such functions as CovarianceFunction, PDF, Probability, and RandomFunction.
New in 9
