Monte Carlo critical values for the time-transformed test (STADF/GSTADF)
Source:R/radf_tt.R
radf_tt_cv.RdThis is the dedicated critical-value function for radf_tt.
It simulates the asymptotic null distribution of the GLS-demeaned
recursive sup-ADF statistic used by radf_tt. Per Theorem 1
of Kurozumi, Skrobotov & Tsarev, this distribution is free of the
volatility process (pivotal), so – unlike radf_wb_cv –
it does not need to be recomputed per dataset: a large n with
default nrep well approximates the T -> Inf limit used in the
paper.
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
The sadf_cv column (STADF, i.e. r1 = 0 fixed) can be checked
against Whitehouse (2019)'s published asymptotic values, quoted in
Kurozumi, Skrobotov & Tsarev's footnote 4: for minw/n = 0.1, (10\
5\
STADF, not GSTADF (gsadf_cv) – the paper's own GSTADF critical
values are not given as literal numbers in the text, only as "easily
computed from" the authors' R code.
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 = 100, minw = 20)
tidy(cv)
#> # A tibble: 3 × 4
#> sig adf sadf gsadf
#> <fct> <dbl> <dbl> <dbl>
#> 1 90 0.889 2.16 2.86
#> 2 95 1.26 2.58 3.22
#> 3 99 2.16 3.28 4.01
# }