Simulate Markov chain Gaussian field

Simulate Markov chain Gaussian field

Usage

mcgf_sim(
  N,
  base = c("sep", "fs"),
  lagrangian = c("none", "lagr_tri", "lagr_askey"),
  par_base,
  par_lagr,
  lambda,
  dists,
  sd = 1,
  lag = 1,
  scale_time = 1,
  horizon = 1,
  init = 0,
  mu_c = 0,
  mu_p = 0,
  return_all = FALSE
)

Arguments

N

Sample size.

base

Base model, sep or fs for now.

lagrangian

Lagrangian model, "none" or lagr_tri for now.

par_base

Parameters for the base model (symmetric).

par_lagr

Parameters for the Lagrangian model.

lambda

Weight of the Lagrangian term, \(\lambda\in[0, 1]\).

dists

Distance matrices or arrays.

sd

Standard deviation for each location.

lag

Time lag.

scale_time

Scale of time unit, default is 1. lag is divided by scale_time.

horizon

Forecast horizon, default is 1.

init

Initial samples, default is 0.

mu_c, mu_p

Means of current and past.

return_all

Logical; if TRUE the joint covariance matrix, arrays of distances and time lag are returned.

Value

Simulated Markov chain Gaussian field with user-specified covariance structure. The simulation is done by kriging. The output data is in space-wide format. dists must contain h for symmetric models, and h1

and h2 for general stationary models. horizon controls forecasting horizon. sd, mu_c, mu_p, and init must be vectors of appropriate sizes.

See also

Other simulations of Markov chain Gaussian fields: mcgf_rs_sim()

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)
dists <- list(h = h, h1 = h1, h2 = h2)

set.seed(123)
X <- mcgf_sim(
    N = 1000, base = "sep", lagrangian = "lagr_tri", lambda = 0.5,
    par_base = par_base, par_lagr = par_lagr, dists = dists
)
plot.ts(X)