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BUILT-IN MATHEMATICA SYMBOL
MAProcess
MAProcess[{b1, ..., bq}, v]
represents a moving-average process of order q with normal white noise that has variance v.
MAProcess[{b1, ..., bq}, 
]
represents a vector moving-average process with multinormal white noise that has covariance matrix .
MAProcess[tproc, q]
gives a moving-average representation of the time series process tproc of order q.
Details
- MAProcess is also known as a finite impulse response (FIR) filter.
- MAProcess is a discrete-time and continuous-state random process.
- The MA process is described by the difference equation
, where 
is the state output, 
is white noise input, and 
is the shift operator. - The scalar MA process has transfer function
, where 
. - The vector MA process has transfer matrix
, where 
, and where 
is the 
×
identity matrix. - A scalar MA process should have real coefficients
and a positive variance v. - An
-dimensional vector MA process should have real coefficient matrices 
of dimensions 
×
, and the covariance matrix should be symmetric positive definite of dimensions 
×
. - Possible time series processes tproc include ARProcess, ARMAProcess, and SARIMAProcess.
- MAProcess[q] gives MAProcess[{
1, ..., q}, 
] for a non-negative integer q. - MAProcess can be used with such functions as CovarianceFunction, PDF, Probability, and RandomFunction.
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