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BUILT-IN MATHEMATICA SYMBOL
ARProcess
ARProcess[{a1, ..., ap}, v]
represents an autoregressive process of order p with normal white noise that has variance v.
ARProcess[{a1, ..., ap}, 
]
represents a vector autoregressive process with multinormal white noise that has covariance matrix .
ARProcess[tproc, p]
approximate a time series process tproc with an AR process of order p.
Details
- ARProcess is a discrete-time and continuous-state random process.
- The AR process is described by the difference equation
,
where 
is the state output, 
is the white noise input, and 
is the shift operator. - The scalar AR process has transfer function
, where 
. - The vector AR process has transfer matrix
, where 
,
and where 
is the 
×
identity matrix. - A scalar AR process should have real coefficients
and a positive variance v. - An
-dimensional vector AR process should have real coefficient matrices 
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.
- ARProcess[p] gives ARProcess[{
1, ..., p}, 
] for a non-negative integer p. - ARProcess can be used with such functions as CovarianceFunction, PDF, Probability, and RandomFunction.
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