ar1sim function

Simulate AR(1) Process

Simulates an autoregressive process of order 1.

ar1sim(n = 50, rho, u0 = 0, var.e = 1, details = FALSE, seed = NULL)

Arguments

• n: total number of observations to be generated (one predetermined start value u0 and n-1 random values)
• rho: true rho value of the AR(1) process to be simulated.
• u0: start value of the process in t = 0.
• var.e: variance of the random error. If zero, no random error is added.
• details: logical value indicating whether details should be printed.
• seed: optionally set a custom random seed for reproducing results.

Returns

A list object including:

u.sim	vector of simulated AR(1) values.
n	total number of simulated AR(1) values.
rho	true rho value of AR(1) process.
e.sim	normal errors in AR(1) process.

Note

Objects generated by ar1sim() can be plotted using the regular plot() command.

plot.what = "time" plots simulated AR(1) values over time. Available options are

...	other arguments that plot() understands.

plot.what = "lag" plots simulated AR(1) values over its lagged values. Available options are

true.line	logical value (default: TRUE). Should the true line be plotted?
acc.line	logical value (default: FALSE). Should the autocorrelation coefficient line be plotted?
ols.line	logical value (default: FALSE). Should the ols regression line be plotted?
...	other arguments that plot() understands.

Examples

## Generate 30 positively autocorrelated errors
my.ar1 <- ar1sim(n = 30, rho = 0.9, var.e = 0.1, seed = 511)
my.ar1
plot(my.ar1$u.sim, type = 'l')

## Illustrate the effect of Rho on the AR(1)
set.seed(12)
parOrg = par(c("mfrow", "mar"))
par(mfrow = c(2,4), mar = c(1,1,1,1))
rhovalues <- c(0.1, 0.5, 0.8, 0.99)
for (i in c(0, 0.3)){
  for (rho in rhovalues){
    u.data <- ar1sim(n = 20, u0 = 2, rho = rho, var.e = i)
    plot(u.data$u.sim, plot.what = "lag", cex.legend = 0.7, xlim = c(-2.5,2.5), ylim = c(-2.5,2.5),
         acc.line = TRUE, ols.line = TRUE)
  }
}
par(mfrow = parOrg$"mfrow", mar = parOrg$"mar")

## Illustrate the effect of Rho on the (non-)stationarity of the AR(1)
set.seed(1324)
parOrg = par(c("mfrow", "mar"))
par(mfrow = c(2, 4), mar = c(1,1,1,1))
for (rho in c(0.1, 0.9, 1, 1.04, -0.1, -0.9, -1, -1.04)){
  u.data <- ar1sim(n = 25, u0 = 5, rho = rho, var.e = 0)
  plot(u.data$u.sim, plot.what = "time", ylim = c(-8,8))
}
par(mfrow = parOrg$"mfrow", mar = parOrg$"mar")