stcfgneiting16 {CoSMoS}

Gneiting-16 SpatioTemporal Correlation Structure

Description

Provides spatiotemporal correlation structure function proposed by Gneiting (2002; Eq.16 at p. 594).

Usage

stcfgneiting16(t, s, a, c, alpha, beta, nu, 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]

nu

smoothness parameter of space. Valid range: >0

tau

space-time interaction parameter. Valid range: \ge 1 (for 2-dimensional fields)

References

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

Examples

library(plot3D)

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

## get the STCS
g16 <- stcfgneiting16(t = st[, 1],
                      s = st[, 2],
                      a = 1/50,
                      c = 1/10,
                      alpha = 1,
                      beta = 1,
                      nu = 0.5, tau = 1)

## visualize the STCS

g16.m <- matrix(g16,
                nrow = d)

persp3D(z = g16.m, x = 1: nrow(g16.m), y = 1:ncol(g16.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))