cor_sep function

Calculate correlation for separable model

cor_sep(
  spatial = c("exp", "cauchy"),
  temporal = c("exp", "cauchy"),
  par_s,
  par_t,
  h,
  u
)

Arguments

• spatial: Pure spatial model, exp or cauchy for now.
• temporal: Pure temporal model, exp or cauchy for now.
• par_s: Parameters for the pure spatial model. Nugget effect supported.
• par_t: Parameters for the pure temporal model.
• h: Euclidean distance matrix or array.
• u: Time lag, same dimension as h.

Returns

Correlations of the same dimension as h and u.

Details

The separable model is the product of a pure temporal model, $C_T(u)$, and a pure spatial model, $C_S(\mathbf{h})$. It is of the form

where $\delta_{x=0}$ is 1 when $x=0$ and 0 otherwise. Here $\mathbf{h}\in\mathbb{R}^2$ and $u\in\mathbb{R}$. Now only exponential and Cauchy correlation models are available.

Examples

h <- matrix(c(0, 5, 5, 0), nrow = 2)
par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5)
u <- matrix(0, nrow = 2, ncol = 2)
par_t <- list(a = 1, alpha = 0.5)
cor_sep(
    spatial = "exp", temporal = "cauchy", par_s = par_s, par_t = par_t,
    h = h, u = u
)

h <- array(c(0, 5, 5, 0), dim = c(2, 2, 3))
par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5)
u <- array(rep(0:2, each = 4), dim = c(2, 2, 3))
par_t <- list(a = 1, alpha = 0.5)
cor_sep(
    spatial = "exp", temporal = "cauchy", par_s = par_s, par_t = par_t,
    h = h, u = u
)

References

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

See Also

Other correlation functions: cor_cauchy(), cor_exp(), cor_fs(), cor_lagr_askey(), cor_lagr_exp(), cor_lagr_tri(), cor_stat(), cor_stat_rs()