Antedependence covariance structure

Antedependence covariance structure. The returned dimensionless covariance shape is intended for use inside vsm, which supplies the single overall variance scale.

Usage

antem(x, order = 1L, beta = NULL, innovations = NULL, fixed = NULL)

Arguments

x

Ordered variable defining q covariance levels.

order

Antedependence order, 1 <= order < q.

beta

Optional starting regression coefficients for allowed subdiagonals.

innovations

Optional q positive innovation variances.

fixed

Logical vector controlling all beta coefficients and q-1 innovation-variance ratios.

Details

The modified-Cholesky representation is $$Ty=e,\qquad \mathrm{Cov}(e)=D,\qquad K=T^{-1}DT^{-\mathsf T}.$$ The matrix \(T\) is unit lower triangular, with nonzero regression coefficients only within the requested number of preceding levels. The first innovation variance is the scale reference; the remaining innovation variances are positive ratios.

Value

A list containing the incidence/design matrix in Z and a compiled CovarianceFactor v2 descriptor in covFactor, for use inside vsm.

See also

ar1m, toeplitzm, vsm.

Examples

if (FALSE) { # \dontrun{
vsm(antem(time, order=2), ism(id))
} # }