longmemo (version 1.1-4)

CetaARIMA: Covariance for fractional ARIMA

Description

Compute the covariance matrix of \(\hat{eta}\) for a fractional ARIMA process.

Usage

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

Value

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

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.

Author

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

Details

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

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)
 ## add row and col names to the cov.matrix (as it is "normal" in R):
 nmC <- c("H", paste0("phi", 1:3), paste0("psi", 1)); dimnames(C.5) <- list(nmC, nmC)
 C.5