Simulate from a random walk order 2 model

rw2sim.R

#Simulate from an RW2 (random walk order 2) model.
# Useful for generating predictions from INLA RW2 models. 
# When forecast, RW2 models predict continuation of trend, with 
# deviations from the trend controlled by the sd parameter.
#
# See: https://inla.r-inla-download.org/r-inla.org/doc/latent/rw2.pdf
# Can intialize the RW2 at a given starting point, this needs
# needs to be two consecutive points, given we are working with
# second order differences. 

rw2sim <- function(n, sd, x0, seed=28937){
  #n: number of time steps
  #sd: sd of the RW2 process
  #X0: starting points, should be length 1 or 2
  # if length 1 then assumes first two starting points
  # are the same
  set.seed(seed)
  z <- rnorm(n, sd = sd)
  x <- numeric(n)
  x[1:2] <- x0
  for (i in 3:n){
    x[i] = z[i] - x[i-2] + 2*x[i-1] 
  }
  x
}