stcfgneiting14 {CoSMoS} R Documentation

## Gneiting-14 SpatioTemporal Correlation Structure

### Description

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

### Usage

```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: ≥ 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
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))

```

[Package CoSMoS version 2.1.0 Index]