Time-Transformed Test for Explosive Bubbles under Non-stationary Volatility

radf_tt computes the STADF/GSTADF test statistics of Kurozumi, Skrobotov & Tsarev, a heteroskedasticity-robust alternative to radf that requires no bootstrap: the series is time-deformed using a nonparametric estimate of its variance profile, after which the usual (asymptotic, homoskedastic) recursive sup-ADF critical values apply.

Usage

radf_tt(data, minw = NULL, kernel = c("uniform", "gaussian"), h = NULL)

Arguments

data: A univariate or multivariate numeric time series object, a numeric vector or matrix, or a data.frame. A column may have leading and/or trailing NA values (an uneven/unbalanced panel where series enter or exit the sample at different times) – those periods are filled with NA in badf/bsadf and excluded from that series' adf/sadf/ gsadf. Interior NA values (a gap in the middle of a series) are not supported. When any series is padded this way, the panel statistic (bsadf_panel/gsadf_panel) is not available and is returned as NA, with a warning.
minw: A positive integer. The minimum window size (default = \((0.01 + 1.8/\sqrt(T))T\), where T denotes the sample size).
kernel: Kernel used in the local variance-profile regression, "uniform" (default, as in the paper's simulations) or "gaussian".
h: Bandwidth for the variance-profile kernel regression. Default T^(-2/5), the midpoint (on the log scale) of the paper's cross-validation search range \([T^{-0.5}, T^{-0.3}]\).

Details

For critical values, use radf_tt_cv as the primary recommendation: it is pivotal (asymptotically free of the volatility process), so it does not need to be recomputed per dataset, unlike a bootstrap. radf_wb_cv (Harvey, Leybourne, Sollis & Taylor's wild bootstrap) is a bootstrap-based alternative, worth considering if non-pivotality/finite-sample bootstrap robustness is a specific concern.

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{
res <- radf_tt(sim_data, minw = 20)
print(res)
#> 
#> ── radf_tt (minw = 20, kernel = uniform) ───────────────────────────────────────
#> 
#>   series      adf    sadf  gsadf
#>     psy1  -1.0366  1.2750  2.204
#>     psy2  -0.8600  2.5960  3.505
#>    evans  -1.3349  1.6556  1.883
#>      div   0.7217  2.3440  2.344
#>     blan  -1.3363  0.4998  1.541
#> 

cv <- radf_tt_cv(n = 100, minw = 20)
summary(res, cv = cv)
#> Error in full_join(tidy(x, format = "long"), tidy(y, format = "long"),     by = c("stat", join_by), relationship = "many-to-many"): Join columns in `y` must be present in the data.
#> ✖ Problem with `id`.
# }