Second-order autoregressive covariance structure

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

Usage

ar2m(x, pacf = c(0.20, 0.10), fixed = NULL,
     variance = c("homogeneous", "heterogeneous"), values = NULL)

Arguments

x: Ordered factor defining covariance levels.
pacf: Length-two vector of starting partial autocorrelations, each strictly between -1 and 1.
fixed: For homogeneous variance, a logical vector of length two. For heterogeneous variance, a logical vector of length q+1: two PACFs followed by q-1 variance-ratio parameters.
variance: Whether the AR correlation has homogeneous or heterogeneous marginal variances.
values: Optional q positive starting variances when variance = "heterogeneous".

Details

A stationary AR(2) covariance is parameterized through reflection coefficients / partial autocorrelations. Each PACF is mapped from an unconstrained working coordinate by tanh, then converted to stable AR coefficients by the Levinson/Durbin recursion. Heterogeneous mode uses $$K=D R D$$ and estimates q-1 positive variance ratios in addition to the PACFs.

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(ar2m(time), ism(id))
} # }