Moving-average covariance structures of order one or two

Moving-average covariance structures of order one or two. The returned dimensionless covariance shape is intended for use inside vsm, which supplies the single overall variance scale.

Usage

mam(x, order = 1L, theta = NULL, fixed = NULL)
ma1m(x, theta = 0.15, fixed = FALSE)
ma2m(x, theta = c(0.15, 0.05), fixed = NULL)

Arguments

x: Ordered factor defining covariance levels.
order: Moving-average order; currently 1 or 2.
theta: Starting MA polynomial coefficients. Defaults to 0.15 for each order.
fixed: Logical vector with one value per MA coefficient.

Details

Using the conventional polynomial \(e_t+\theta_1e_{t-1}+\theta_2e_{t-2}\), the autocovariance at lag \(h\) is proportional to \(\sum_{j=0}^{p-h}\theta_j\theta_{j+h}\) with \(\theta_0=1\). The covariance is normalized to correlation scale and is zero beyond lag \(p\). Invertibility of the MA polynomial is not required merely to define this covariance matrix. ma1m and ma2m are convenience wrappers.

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(ma1m(time), ism(id))
vsm(ma2m(time), ism(id))
} # }