Q.AR1 {ar.matrix}

Precision matrix for an AR1 process

Description

Functions for creating precision matricies and observations of an AR1 process

Usage

Q.AR1(M, sigma, rho, sparse=FALSE, vcov=FALSE)

r.AR1(n, M, sigma, rho)

Arguments

M

int > 0, number of elements in the AR1 process.

sigma

float > 0, pairwise observation standard deviation.

rho

float >= 0 & < 1, how correlated pairwise observations are. The function will still run with values outside of the range [0,1) however the stability of the simulation results are not gaurunteed.

sparse

bool Should the matrix be of class 'dsCMatrix'

vcov

bool If the vcov matrix should be returned instead of the precision matrix.

n

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

Value

Q.AR1 returns either a precision or variance-covariance function with a AR1 structure.

r.AR1 retrurns a matrix with n rows which are the n observations of a Gaussian Markov random field AR1 process.

Examples

require("ggplot2")
# simulate AR1 GMRF
obs <- r.AR1(100, M=30, sigma=1, rho=.98)
# resulting matrix is n x M
dim(obs)
# subtract off the first time point to more easily observe correlation
obs_adj <- obs - obs[,1]
# move objects to a data frame
ar1_df <- data.frame(obs=c(t(obs_adj)), realization=rep(1:100, each=30),
                     time=rep(1:30, 100))
# plot each realization
ggplot(data=ar1_df, aes(time, obs, group=realization, color=realization)) +
    geom_line()