- FARIMAProcess is also known as ARFIMA or long-memory time series.
- FARIMAProcess is a discrete-time and continuous-state random process.
- The FARIMA process is described by the difference equations , where is the state output, is the white noise input, and is the shift operator.
- The scalar FARIMA process has transfer function , where .
- The vector FARIMA process has transfer matrix , where , and where is the × identity matrix.
- A scalar FARIMA process should have real coefficients , , real integrating parameter d such that , and a positive variance v.
- An -dimensional vector FARIMA process should have real coefficient matrices and of dimensions ×, real integrating parameters such that or real integrating parameter d such that , and the covariance matrix Σ should be symmetric positive definite of dimensions ×.
- FARIMAProcess[p,d,q] and FARIMAProcess[p,q] represent a FARIMA process of orders p and q with known or unknown integration order d for use in EstimatedProcess and related functions.
- FARIMAProcess can be used with such functions as CovarianceFunction, RandomFunction, and TimeSeriesForecast.
Introduced in 2012