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.


  • 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[{FormalB1, ..., FormalBq}, FormalV] for a non-negative integer q.
  • MAProcess can be used with such functions as CovarianceFunction, PDF, Probability, and RandomFunction.
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