Third-order autoregressive covariance structure

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

Usage

ar3m(x, pacf = c(0.20, 0.10, 0.05), fixed = NULL,
     variance = c("homogeneous", "heterogeneous"), values = NULL)

Arguments

x: Ordered factor defining covariance levels.
pacf: Length-three vector of starting partial autocorrelations, each strictly between -1 and 1.
fixed: For homogeneous variance, a logical vector of length three. For heterogeneous variance, a logical vector of length q+2: three 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(3) covariance is parameterized through three partial autocorrelations. The PACF parameterization guarantees stationarity while allowing unconstrained working coordinates. 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(ar3m(time), ism(id))
} # }