General positive-definite Toeplitz correlation structure

General positive-definite Toeplitz correlation structure. The returned dimensionless covariance shape is intended for use inside vsm, which supplies the single overall variance scale.

Usage

toeplitzm(x, pacf = NULL, fixed = NULL)

Arguments

x: Ordered factor or design defining q covariance levels.
pacf: Optional q-1 starting reflection coefficients / partial autocorrelations. Defaults to 0.10.
fixed: Logical vector of length q-1.

Details

A full q by q Toeplitz correlation matrix is parameterized by q-1 reflection coefficients. Each PACF is mapped from an unconstrained working coordinate with tanh; the reflection coefficients are converted to a stable autoregressive representation and then to the implied Toeplitz correlation sequence. This parameterization preserves positive definiteness while allowing every lag correlation to vary indirectly.

Value

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

Examples

if (FALSE) { # \dontrun{
vsm(toeplitzm(time), ism(id))
} # }