Heteroskedasticity-robust (time-transformed)

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

radf_tt

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

radf_tt computes the STADF and GSTADF test statistics of Kurozumi, Skrobotov & Tsarev, a heteroskedasticity-robust alternative to radf that needs no bootstrap. It time-deforms the series with a nonparametric estimate of its variance profile, after which the usual asymptotic recursive sup-ADF critical values for homoskedastic errors apply.

Arguments

data	A univariate or multivariate numeric time series object, a numeric vector or matrix, or a data.frame. A column may have leading or trailing `NA` values, which describes an unbalanced panel in which series enter or exit the sample at different times. Those periods are filled with `NA` in `badf` and `bsadf` and excluded from the `adf`, `sadf` and `gsadf` of that series. Interior `NA` values (a gap in the middle of a series) are not supported. When any series is padded in this way, the panel statistics (`bsadf_panel` and `gsadf_panel`) are not available, and the function returns `NA` for them 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 simulations of the paper) or `"gaussian"`.
h	Bandwidth for the variance-profile kernel regression. The default is `T^(-2/5)`, the midpoint on the log scale of the cross-validation search range $[T^{-0.5}, T^{-0.3}]$ of the paper.

Value

An object of class radf_tt_obj/radf_obj: the same adf/badf/sadf/bsadf/gsadf list as for radf, computed on the time-transformed series. It works with summary(), datestamp(), tidy() and autoplot() when paired with radf_tt_cv.

Details

We recommend radf_tt_cv for the critical values. They are pivotal (asymptotically free of the volatility process), so they do not have to be recomputed for each dataset, unlike a bootstrap. The wild bootstrap of Harvey, Leybourne, Sollis & Taylor in radf_wb_cv is a bootstrap-based alternative. Consider it if non-pivotality or the finite-sample robustness of the bootstrap is a specific concern.

Status

[Experimental]

Examples

These examples are copied from the package's own documentation and are run by R CMD check on every release. The printed output (after #>) and the plots were produced by running them against the current package source.

# 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)
print(res)
#> 
#> ── radf_tt (minw = 20, kernel = uniform) ───────────────────────────────────────
#> 
#>    series      adf   sadf  gsadf
#>   series1  -0.9972  3.275  4.229

cv <- radf_tt_cv(n = 200, minw = 20)
summary(res, cv = cv)
#> 
#> ── Summary (minw = 20, lag = 0) ────────── Time-Transformed MC (nboot = 2000) ──
#> 
#> series1 :
#> # A tibble: 3 × 5
#>   stat   tstat  `90`  `95`  `99`
#>   <fct>  <dbl> <dbl> <dbl> <dbl>
#> 1 adf   -0.997 0.833  1.21  1.97
#> 2 sadf   3.27  2.31   2.65  3.35
#> 3 gsadf  4.23  3.27   3.65  4.42
tidy(res, cv = cv)
#> # A tibble: 1 × 4
#>   id         adf  sadf gsadf
#>   <fct>    <dbl> <dbl> <dbl>
#> 1 series1 -0.997  3.27  4.23
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)

References

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