ARIMAProcess

ARIMAProcess[{a1,,ap},d,{b1,,bq},v]
represents an autoregressive integrated moving-average process such that its ^(th) difference is a weakly stationary ARMAProcess[{a1,,ap},{b1,,bq},v].

ARIMAProcess[{a1,,ap},d,{b1,,bq},Σ]
represents a vector ARIMA process such that its ^(th) difference is a vector weakly stationary ARMAProcess.

ARIMAProcess[{a1,,ap},{d1,,dn},{b1,,bq},Σ]
represents a vector ARIMA process such that its ^(th) difference is a vector weakly stationary ARMAProcess.

ARIMAProcess[{a1,,ap},d,{b1,,bq},v,init]
represents an ARIMA process with initial data init.

ARIMAProcess[c,]
represents an ARIMA process with a constant c.

DetailsDetails

  • ARIMAProcess is a discrete-time and continuous-state random process.
  • An ARIMAProcess[,d,,v] has a polynomial trend of degree d for d1.
  • The ARIMA process is described by the difference equation , where is the state output, is the 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 ARIMA process should have real coefficients , , and c, non-negative integer integration order d, and a positive variance v.
  • An -dimensional vector ARIMA process should have real coefficient matrices and of dimensions ×, real vector c of length , integer non-negative integrating orders or integer non-negative integrating order d, and the covariance matrix Σ should be symmetric positive definite of dimensions ×.
  • The ARIMA process with zero constant has transfer function , where , , and where is an -dimensional unit.
  • ARIMAProcess[p,d,q] represents an ARIMA process with autoregressive and moving average orders p and q and integration order d for use in EstimatedProcess and related functions.
  • ARIMAProcess can be used with such functions as CovarianceFunction, RandomFunction, and TimeSeriesForecast.
Introduced in 2012
(9.0)
| Updated in 2014
(10.0)