Simulate innovations with heavy-tailed/skewed marginal distributions

sim_innov(
  n,
  dist = c("normal", "t", "skew_t"),
  sigma = 6.79,
  df = 5,
  xi = 0,
  seed = NULL
)

Generates a shock sequence for use with the PSY-style mean equations (sim_psy1 and sim_psy2) but with a non-Gaussian marginal distribution. The sequence is standardized to mean 0 and variance sigma^2, so it fits directly into sim_psy1(..., e = sim_innov(...)).

Arguments

n	Number of innovations to generate.
dist	One of "normal", "t", "skew_t".
sigma	A positive scalar indicating the standard deviation of the innovations.
df	Degrees of freedom for "t"/"skew_t" (> 2).
xi	Skewness parameter for "skew_t" (any real; 0 = symmetric).
seed	An object specifying if and how the random number generator (rng) should be initialized. It is either NULL or an integer, which is passed to set.seed before the simulation. If you set it, the value is saved as the "seed" attribute of the returned value. The default, NULL, leaves the state of the rng unchanged and returns .Random.seed as the "seed" attribute. Results are reproducible across the parallel and the non-parallel option when you use the same seed.

Value

A numeric vector of length n.

Details

dist = "t" rescales a Student-t(df) draw to variance 1 before scaling by sigma. This is exact and closed form, because Var(t_df) = df / (df - 2). dist = "skew_t" combines two independent standardized Student-t draws in the manner of Azzalini, delta * abs(T0) + sqrt(1 - delta^2) * T1 with delta = xi / sqrt(1 + xi^2), and then standardizes the result with the closed-form mean and variance of that combination (E|T0| is itself closed form through the Beta function). xi > 0 skews the distribution to the right, xi < 0 skews it to the left, and xi = 0 gives the symmetric t case.

sim_innov(199, dist = "skew_t", df = 3, xi = -0.75, seed = 1) %>%
  autoplot()

# Feed skew-t innovations into sim_psy1() in place of i.i.d. Gaussian ones
sim_psy1(n = 200, seed = 123, e = sim_innov(199, dist = "skew_t", df = 3, xi = -0.75, seed = 1)) %>%
  autoplot()