I’d like to simulate an AR(1) time series that approximates a gamma distribution rather than a normal distribution. I’d like the result to have a specified rate and shape along with a AR(1) process with a given phi. I have seen this post and understand that a strict gamma simulation is problematic, but I'd be satisfied with a result that approximates the shape and rate. Some crude adjustment of shape and rate as a function of phi is likely enough for my needs. Any idea?
E.g.,
n <- 500
foo <- rgamma(n = n, shape = 1.5 , rate = 5)
phi <- 0.3
bar <- arima.sim(list(order = c(1,0,0), ar = phi), n = n,
rand.gen = rgamma, shape = 1.5,
rate = 5)
ggplot() +
geom_density(aes(x=foo),fill="#FF8C00",alpha=0.5) +
geom_density(aes(x=bar),fill="#A034F0",alpha=0.5)
