R/simAR.R

In ar.matrix: Simulate Auto Regressive Data from Precision Matricies

#' Simulate correlated data from a precision matrix.
#'
#' @description Takes in a square precision matrix, which ideally should be
#' sparse and using Choleski factorization simulates data from a mean 0 process
#' where the inverse of the precision matrix represents the variance-covariance
#' of the points in the process. The resulting simulants represent samples of a
#' Gaussian Markov random field (GMRF).
#'
#' @param n int > 0, number of observations to simulate from the GMRF.
#' @param Q matrix, a square precision matrix.
#'
#' @return Matrix object, matrix where each row is a single obsrevation from
#' a GMRF with covariance structure Q^-1.
#'
#' @examples
#' require("ggplot2")
#'
#' # simulate 2D ar1 process
#' # pairwise correlation
#' rho <- .95
#' # pairwise variance
#' sigma <- .5
#'
#' # 2 dimensions of simulations
#' years <- 20
#' ages <- 10
#'
#' # kronnecker product to get joint covariance
#' Q2D <- kronecker(Q.AR1(M=years, sigma, rho), Q.AR1(M=ages, sigma, rho))
#'
#' # simulate the data and place it in a data frame
#' Q2D.df <- data.frame(obs=c(sim.AR(1, Q2D)), age=rep(1:ages, years),
#'                      year=rep(1:years, each=ages))
#'
#' # graph results
#' ggplot(data=Q2D.df, aes(year, obs, group=age, color=age)) + geom_line()
#'
#' @export

sim.AR <- function(n, Q){
    sparseMVN::rmvn.sparse(
        n,
        rep(0, nrow(Q)),
        Matrix::Cholesky(Matrix::Matrix(Q, sparse=TRUE)), T)
}