Simulate innovations with a permanent volatility break

Generates i.i.d. Gaussian shocks whose standard deviation shifts permanently from sigma to sigma * ratio at observation tau * n, for use as sim_psy1(..., e = sim_vol_break(...)). This is the non-stationary volatility DGP (Cavaliere & Taylor 2007's single break) under which radf's standard critical values lose size control, and the one the volatility-robust tests (radf_tt, radf_kp, radf_sbz, radf_sign, radf_wb_cv) are designed for – unlike stationary conditional heteroskedasticity (sim_vol_garch), whose variance profile is asymptotically flat.

Usage

sim_vol_break(n, tau = 0.5, ratio = 3, sigma = 6.79, seed = NULL)

Arguments

n: Number of innovations to generate.
tau: Break fraction in (0, 1): the shift happens after observation floor(tau * n).
ratio: Positive post-/pre-break standard deviation ratio; ratio > 1 is an upward break (the case where radf() over-rejects most), ratio < 1 a downward one.
sigma: A positive scalar indicating the standard deviation of the innovations.
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.

References

Cavaliere, G. & Taylor, A.M.R. (2007). "Testing for unit roots in time series models with non-stationary volatility." Journal of Econometrics, 140, 919-947. Harvey, D.I., Leybourne, S.J., Sollis, R. & Taylor, A.M.R. (2016). "Tests for explosive financial bubbles in the presence of non-stationary volatility." Journal of Empirical Finance, 38, 548-574.

Examples

sim_vol_break(199, seed = 1) %>%
  autoplot()

# Volatility triples half-way through a PSY bubble series
sim_psy1(n = 200, seed = 123, e = sim_vol_break(199, seed = 123)) %>%
  autoplot()