cor_stat function

Calculate general stationary correlation.

cor_stat(
  base = c("sep", "fs"),
  lagrangian = c("none", "lagr_tri", "lagr_askey"),
  par_base,
  par_lagr,
  lambda,
  h,
  h1,
  h2,
  u,
  base_fixed = FALSE
)

Arguments

• base: Base model, sep or fs for now. Or correlation matrix/array.
• lagrangian: Lagrangian model, none, lagr_tri, or lagr_askey.
• par_base: Parameters for the base model (symmetric), used only when base_fixed = FALSE.
• par_lagr: Parameters for the Lagrangian model. Used only when lagrangian is not none.
• lambda: Weight of the Lagrangian term, $\lambda\in[0, 1]$.
• h: Euclidean distance matrix or array, used only when base_fixed = FALSE.
• h1: Horizontal distance matrix or array, same dimension as h. Used only when lagrangian is not none.
• h2: Vertical distance matrix or array, same dimension as h. Used only when lagrangian is not none.
• u: Time lag, same dimension as h.
• base_fixed: Logical; if TRUE, base is the correlation.

Returns

Correlations for the general stationary model. Same dimension of base if base_fixed = FALSE.

Details

The general station model, a convex combination of a base model and a Lagrangian model, has the form

where $\lambda$ is the weight of the Lagrangian term.

If base_fixed = TRUE, the correlation is of the form

where base is a correlation matrix/array and par_base and h are not used.

When lagrangian = "none", lambda must be 0.

Examples

par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5)
par_t <- list(a = 1, alpha = 0.5)
par_base <- list(par_s = par_s, par_t = par_t)
par_lagr <- list(v1 = 5, v2 = 10)
h1 <- matrix(c(0, 5, -5, 0), nrow = 2)
h2 <- matrix(c(0, 8, -8, 0), nrow = 2)
h <- sqrt(h1^2 + h2^2)
u <- matrix(0.1, nrow = 2, ncol = 2)
cor_stat(
    base = "sep", lagrangian = "lagr_tri", par_base = par_base,
    par_lagr = par_lagr, lambda = 0.8, h = h, h1 = h1, h2 = h2, u = u
)

h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3))
h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3))
h <- sqrt(h1^2 + h2^2)
u <- array(rep(c(0.1, 0.2, 0.3), each = 4), dim = c(2, 2, 3))
fit_base <- cor_fs(
    nugget = 0.5, c = 0.01, gamma = 0.5, a = 1, alpha = 0.5,
    beta = 0.0, h = h, u = u
)
par_lagr <- list(v1 = 5, v2 = 10)
cor_stat(
    base = fit_base, lagrangian = "lagr_askey", par_lagr = par_lagr,
    h1 = h1, h2 = h2, u = u, lambda = 0.8, base_fixed = TRUE
)

See Also

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