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BUILT-IN MATHEMATICA SYMBOL
ARMAProcess
ARMAProcess[{a1, ..., ap}, {b1, ..., bq}, v]
represents an autoregressive moving-average process with AR coefficients 
, MA coefficients 
, and normal white noise variance v.
ARMAProcess[{a1, ..., ap}, {b1, ..., bq}, 
]
represents the vector autoregressive moving-average process with coefficient matrices 
and 
and covariance matrix .
ARMAProcess[tproc]
attempts to give the ARMA representation of tproc.
ARMAProcess[tproc, {p, q}]
approximates a time series process tproc with an ARMA process of orders p and q.
Details
- ARMAProcess is a discrete-time and continuous-state random process.
- The ARMA process is described by the difference equation
,
where 
is the state output, 
is white noise input, and 
is the shift operator. - The scalar ARMA process has transfer function
, where 
. - The vector ARMA process has transfer matrix
, where 
, and where 
is the 
×
identity matrix. - A scalar ARMA process should have real coefficients
and 
and a positive variance v. - An
-dimensional vector ARMA process should have real coefficient matrices 
and 
of dimensions 
×
, and the covariance matrix should be symmetric positive definite of dimensions 
×
. - The following time series processes tproc can be approximated: MAProcess, ARProcess, ARMAProcess, ARIMAProcess, FARIMAProcess, and SARIMAProcess.
- ARMAProcess[p, q] gives ARMAProcess[{
1, ..., p}, {
1, ..., q}, 
] for non-negative integers p and q. - ARMAProcess can be used with such functions as CovarianceFunction, PDF, Probability, and RandomFunction.
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