represents an ARIMA process with initial data init.
represents an ARIMA process with a constant c.
- ARIMAProcess is a discrete-time and continuous-state random process.
- An ARIMAProcess[…,d,…,v] has a polynomial trend of degree d for d≥1.
- 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