represents a moving-average process of order q with normal white noise variance v.

represents a vector MA process with multinormal white noise covariance matrix Σ.

represents an MA process with initial data init.

represents an MA process with a constant c.


  • 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, is the shift operator, and the constant c is taken to be zero if not specified.
  • The initial data init can be given as a list or a single-path TemporalData object with time stamps understood as .
  • A scalar MA process should have real coefficients and c, and a positive variance v.
  • An -dimensional vector MA process should have real coefficient matrices of dimensions ×, real vector c of length , and the covariance matrix Σ should be symmetric positive definite of dimensions ×.
  • The MA process with zero constant has transfer function where:
  • scalar process
    vector process; is the × identity matrix
  • MAProcess[tproc,q] for a time series process tproc gives an MA process of order q such that the series expansions about zero of the corresponding transfer functions agree up to degree q.
  • Possible time series processes tproc include ARProcess, ARMAProcess, and SARIMAProcess.
  • MAProcess[q] represents a moving-average process of order q for use in EstimatedProcess and related functions.
  • MAProcess can be used with such functions as CovarianceFunction, RandomFunction, and TimeSeriesForecast.
Introduced in 2012
| Updated in 2014
Translate this page: