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.

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Simulate an MA process:

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Covariance function:

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Correlation function:

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Partial correlation function:

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