Simulation of a mixed causal-noncausal AR(1,1) bubble

sim_mar(
  n,
  phi1 = 0.7,
  psi1 = 0.7,
  dist = c("cauchy", "t"),
  df = 2,
  burn = 100,
  seed = NULL
)

Simulates the mixed causal-noncausal autoregressive (MAR) bubble process of Blasques, Koopman, Mingoli & Telg (2025). Transient, self-terminating local bubbles arise on their own from the noncausal (forward-looking) component. Unlike sim_psy1, no origination or collapse dates are scripted.

Arguments

n	A positive integer specifying the length of the simulated output series.
phi1	Causal AR coefficient, in (0, 1).
psi1	Noncausal AR coefficient, in (0, 1).
dist	Innovation distribution: "cauchy" or "t" (with df degrees of freedom).
df	Degrees of freedom if dist = "t".
burn	Non-negative burn-in length applied at both ends (see Details).
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

$$(1-\phi_1 L)(1-\psi_1 L^{-1})y_t = \epsilon_t$$

The function uses the standard two-sided filtering method for MAR processes (Lanne & Saikkonen 2011; Gourieroux & Zakoian 2017). It generates the noncausal component by running $u_t=\psi_1 u_{t+1}+\epsilon_t$ backward from a zero boundary burn observations past the end of the sample. It then generates the causal component by running $y_t=\phi_1 y_{t-1}+u_t$ forward from a zero boundary burn observations before the start. Both burn-in windows are then dropped.

sim_mar(200, seed = 123) %>%
  autoplot()