Monte Carlo critical values for the time-transformed test (STADF/GSTADF)

This is the dedicated critical-value function for radf_tt. It simulates the asymptotic null distribution of the GLS-demeaned recursive sup-ADF statistic that radf_tt uses. By Theorem 1 of Kurozumi, Skrobotov & Tsarev, this distribution is free of the volatility process (pivotal). Unlike radf_wb_cv, it therefore does not have to be recomputed for each dataset. A large n with the default nrep approximates well the T -> Inf limit used in the paper.

Usage

radf_tt_cv(n, minw = NULL, nrep = 2000L, seed = NULL)

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. 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

An object of class radf_cv/tt_cv/mc_cv with the same structure as radf_mc_cv: the scalars adf_cv, sadf_cv and gsadf_cv for each level plus the sequences badf_cv and bsadf_cv. You can use it wherever a radf_cv is accepted.

Details

You can check the sadf_cv column (STADF, that is, r1 = 0 fixed) against the asymptotic values of Whitehouse (2019) quoted in footnote 4 of Kurozumi, Skrobotov & Tsarev. For minw/n = 0.1, the values at (10\ 1\ GSTADF (gsadf_cv). The paper gives its GSTADF critical values not as numbers in the text but only as "easily computed from" the code of the authors in R.

Note

Since 2026-08-18 the function also computes badf_cv and bsadf_cv, a time-varying boundary with one row for each recursion point. datestamp and autoplot therefore work on radf_tt results, and not only summary() and tidy. The bsadf_cv of radf_mc_cv is a cummax() across replicates, which works around the output shape of the base C++ engine. Here no such shortcut is needed, because the bsadf of gls_dfstat_grid() (internal) is already the sup over all window starts at each point, and the boundary is the per-time-point quantile across replicates. We validated the function in three ways. The last row of badf_cv is bit-identical to adf_cv, an exact identity because adf is the last point of badf in every replicate. The empirical false-alarm rate under H0 is conservative relative to the nominal level (3.3\ power on a synthetic bubble matches the established radf() and radf_mc_cv() pipeline almost exactly (18\ series. radf_sign_cv() and radf_sign_dm_cv() now compute the same boundary (see vignette("naming-and-analysis")).

Status

References

Kurozumi, E., Skrobotov, A., & Tsarev, A. (2024). Time-Transformed Test for Bubbles under Non-stationary Volatility. Journal of Financial Econometrics. doi:10.1093/jjfinec/nbae026

Examples

# \donttest{
cv <- radf_tt_cv(n = 200, minw = 20)
tidy(cv)
#> # A tibble: 3 × 4
#>   sig     adf  sadf gsadf
#>   <fct> <dbl> <dbl> <dbl>
#> 1 90    0.899  2.35  3.32
#> 2 95    1.34   2.63  3.67
#> 3 99    1.97   3.27  4.39

# Volatility triples half-way through the sample. This is the case of
# non-stationary volatility that this test is built for, and plain radf()
# over-rejects here
y <- sim_psy1(n = 200, seed = 1, e = sim_vol_break(199))
res <- radf_tt(y, minw = 20)
datestamp(res, cv = cv)
#> 
#> ── Datestamp (min_duration = 0) ───────────────────────── Time-Transformed MC ──
#> 
#> series1 :
#>   Start Peak End Duration   Signal Ongoing
#> 1    21   38  89       68 negative   FALSE
#> 2   148  148 149        1 positive   FALSE
#> 
autoplot(res, cv = cv)

# }