stcfgneiting14 function

Gneiting-14 SpatioTemporal Correlation Structure

Provides spatiotemporal correlation structure function proposed by Gneiting (2002; Eq.14 at p. 593).

stcfgneiting14(t, s, a, c, alpha, beta, gamma, tau)

Arguments

• t: time lag
• s: spatial lag (distance)
• a: nonnegative scaling parameter of time
• c: nonnegative scaling parameter of space
• alpha: smoothness parameter of time. Valid range: $(0,1]$
• beta: space-time interaction parameter. Valid range: $[0,1]$
• gamma: smoothness parameter of space. Valid range: $(0,1]$
• tau: space-time interaction parameter. Valid range: $\ge 1$ (for 2-dimensional fields)

Examples

library(plot3D)

## specify grid of spatial and temporal lags
d <- 31
st <- expand.grid(0:(d - 1),
                  0:(d - 1))

## get the STCS
g14 <- stcfgneiting14(t = st[, 1],
                      s = st[, 2],
                      a = 1/50,
                      c = 1/10,
                      alpha = 1,
                      beta = 1,
                      gamma = 0.5,
                      tau = 1)

## visualize the STCS

g14.m <- matrix(g14,
                nrow = d)

persp3D(z = g14.m, x = 1: nrow(g14.m), y = 1:ncol(g14.m),
        expand = 1, main = "", scale = TRUE, facets = TRUE,
        xlab="Time lag", ylab = "Distance", zlab = "STCF",
        colkey = list(side = 4, length = 0.5), phi = 20, theta = 120,
        resfac = 5,  col= gg2.col(100))

References

Gneiting, T. (2002). Nonseparable, Stationary Covariance Functions for Space-Time Data, Journal of the American Statistical Association, 97:458, 590-600, tools:::Rd_expr_doi("10.1198/016214502760047113")