sim.AR {ar.matrix}

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).

Usage

sim.AR(n, Q)

Arguments

n

int > 0, number of observations to simulate from the GMRF.

Q

matrix, a square precision matrix.

Value

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()