Simulates the asymptotic null distribution of radf_sign's
statistic. Per Theorem 2 of Harvey, Leybourne & Zu (2020), this
distribution does not depend on the volatility process at all (exact
invariance) – so, like radf_tt_cv and unlike
radf_wb_cv, it does not need to be recomputed per
dataset: a large n with the default nrep approximates the
paper's own T -> Inf limit.
Arguments
- n
A positive integer. The sample size.
- minw
A positive integer. The minimum window size (default = \((0.01 + 1.8/\sqrt(T))T\), where T denotes the sample size).
- nrep
A positive integer. The number of Monte Carlo simulations.
- 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.seedbefore 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.
Details
sadf_cv (single-supremum, r1 = 0 fixed) can be checked
against the paper's Table 1 asymptotic (T = Inf) sPWY values:
for minw/n = 0.1, (10\
gsadf_cv (double-supremum) corresponds to the sPSY row:
(2.933, 3.180, 3.655).
![[Experimental]](figures/lifecycle-experimental.svg)
References
Harvey, D. I., Leybourne, S. J., & Zu, Y. (2020). Sign-based unit root tests for explosive financial bubbles in the presence of deterministically time-varying volatility. Econometric Theory, 36(1), 122-169.
Examples
# \donttest{
cv <- radf_sign_cv(n = 100, minw = 20)
tidy(cv)
#> # A tibble: 3 × 4
#> sig adf sadf gsadf
#> <fct> <dbl> <dbl> <dbl>
#> 1 90 0.885 2.27 2.93
#> 2 95 1.34 2.61 3.38
#> 3 99 1.96 3.25 4.38
# }