CetaARIMA: Covariance for fractional ARIMA

In longmemo: Statistics for Long-Memory Processes (Book Jan Beran), and Related Functionality

Description

Compute the covariance matrix of eta^ for a fractional ARIMA process.

Usage

CetaARIMA(eta, p, q, m = 10000, delta = 1e-9)

Arguments

eta	parameter vector eta = c(H, phi, psi).
p,q	integer scalars giving the AR and MA order respectively.
m	integer specifying the length of the Riemann sum, with step size 2 * pi/m.
delta	step size for numerical derivative computation.

Details

builds on calling specARIMA(eta,p,q,m)

Value

the (square) matrix containg covariances up to ...

Author(s)

Jan Beran (principal) and Martin Maechler (fine tuning)

References

Beran(1984), listing on p.224–225.

Examples

 (C.7  <- CetaARIMA(0.7, m = 256, p = 0, q = 0))
 (C.5  <- CetaARIMA(eta = c(H = 0.5, phi=c(-.06, 0.42, -0.36), psi=0.776),
                    m = 256, p = 3, q = 1))

Example output

          [,1]
[1,] 0.7163357
           [,1]       [,2]       [,3]       [,4]       [,5]
[1,]  3.3963350 -2.1019885 -2.4048012  0.1053109 -0.8301053
[2,] -2.1019885  3.5743701  1.0035697 -0.6869983 -1.1009386
[3,] -2.4048012  1.0035697  2.7727059  0.2182855  1.3808039
[4,]  0.1053109 -0.6869983  0.2182855  0.9250799  0.2104931
[5,] -0.8301053 -1.1009386  1.3808039  0.2104931  2.0905384

longmemo documentation built on March 26, 2020, 7:42 p.m.