MAProcess

MAProcess[{b1,,bq},v]

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

MAProcess[{b1,,bq},Σ]

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

MAProcess[{b1,,bq},v,init]

represents an MA process with initial data init.

MAProcess[c,]

represents an MA process with a constant c.

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, 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 {,y[-2],y[-1]} or a single-path TemporalData object with time stamps understood as {,-2,-1}.
• A scalar MA process should have real coefficients bi and c, and a positive variance v.
• An -dimensional vector MA process should have real coefficient matrices bi 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.

Examples

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Basic Examples(3)

Simulate an MA process:

 In:= Out= In:= Out= Covariance function:

 In:= Out= In:= Out= Correlation function:

 In:= Out= Partial correlation function:

 In:= Out= Neat Examples(2)

Introduced in 2012
(9.0)
|
Updated in 2014
(10.0)