Simulation of a deterministic technology-adoption "false bubble" null

Simulation of Chen, Chen, Huang, Li & Zhang (2026)'s false-bubble DGP: a hump-shaped, deterministic technology-adoption shock embedded in dividend growth, engineered so a Campbell-Shiller present-value fundamental alone – with no bubble component at all – displays a locally explosive-looking price path. Useful as a null (no-bubble) stress test distinct from a plain random walk.

Usage

sim_falsebubble(
  n,
  t1 = floor(0.3 * n),
  t2 = floor(0.7 * n),
  kappa = floor((t2 - t1)/2),
  shape = c("triangular", "gaussian"),
  amplitude = 1,
  mu = 0.02,
  sigma_d = 0.05,
  r = 0.05,
  d0 = 0,
  seed = NULL
)

Arguments

n: A positive integer specifying the length of the simulated output series.
t1: Adoption (ramp-up start) date, in 1:n.
t2: Maturation (shock end) date, in t1:n.
kappa: Peak lag (time from t1 to the hump's peak), in 0:(t2 - t1).
shape: "triangular" (default) or "gaussian".
amplitude: A positive scalar scaling the hump's peak height.
mu: A scalar, the baseline dividend-growth drift.
sigma_d: A positive scalar, the dividend-growth innovation standard deviation.
r: A positive scalar, the discount rate.
d0: Starting (log) dividend level.
seed: An object specifying if and how the random number generator (rng) should be initialized. Either NULL or an integer will be used in a call to set.seed before simulation. If set, the value is saved as "seed" attribute of the returned value. The default, NULL, will not change rng state, and return .Random.seed as the "seed" attribute. Results are reproducible across the parallel and non-parallel option when the same seed is used.

Value

A numeric vector of length n (the price), with "dividend" and "technology" attributes.

Details

Dividends follow a random walk with drift plus the technology hump: \(d_t = d_{t-1}+\mu+\tau_t+\eta_t\). The hump \(\tau_t\) rises linearly from t1 to t1 + kappa then falls linearly to t2 (shape = "triangular", the source's own worked example, eq. 4), or follows a Gaussian bump centered at t1 + kappa (shape = "gaussian"). Because \(\tau_t\) is deterministic (known in advance), its contribution to the price is an exact forward-looking discounted sum, \(T_t=\sum_{s>t}\beta^{s-t}\tau_s\) with \(\beta=1/(1+r)\), added to the same fundamental pricing formula sim_div uses. This is a simplified, single-shock reproduction of the source's mechanism (deterministic hump -> hump-shaped fundamental price, no bubble), not its full DOLS/ multiple-functional-form robustness machinery.

References

Chen, H., Chen, L., Huang, D., Li, Y. & Zhang, Z. (2026). "Technology Fundamentals and False Bubble Detection: Evidence from Dot-Com and AI Episodes." arXiv:2604.25826.

Examples

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