Wild Bootstrap Critical Values for the SBZ Statistic

radf_sbz_cv performs the HLST (2016) wild bootstrap. It is the same algorithm as radf_wb_cv, applied to the WLS/kernel-volatility statistic of radf_sbz instead of the classic supDF statistic. It generates critical values that include the time-varying badf_cv and bsadf_cv boundary that datestamp and autoplot need, and not only the three scalar critical values that summary() uses.

Usage

radf_sbz_cv(
  data,
  minw = NULL,
  nboot = 499L,
  kernel = c("gaussian", "uniform"),
  h = NULL,
  seed = 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 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).

nboot

A positive integer. Number of bootstraps (default = 500L).

kernel

Kernel for the spot-volatility estimator (eq. 6 of Harvey, Leybourne & Zu 2019), "gaussian" (default, as in the paper) or "uniform".

h

Bandwidth for the spot-volatility estimator. The default is leave-one-out cross-validation over the search range of the paper.

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/sbz_cv/wb_cv: a list with the critical values adf_cv, sadf_cv and gsadf_cv (one row per series) and badf_cv and bsadf_cv (one array per series, one row per recursion point).

Status

References

Harvey, D. I., Leybourne, S. J., & Zu, Y. (2019). Testing explosive bubbles with time-varying volatility. Econometric Reviews, 38(10), 1131-1151.

See also

radf_sbz for the statistic that this function pairs with, and radf_sbz_union for the bundled union-of-rejections test against the classic supDF statistic. You cannot obtain that test from this function and radf_wb_cv separately (see the Details of radf_sbz_union for why).

Other critical values: radf_common_cv(), radf_mc_cv(), radf_recovery_cv(), radf_sb_cv(), radf_sign_cv(), radf_sign_dm_cv(), radf_tt_cv(), radf_wb_cv(), radf_wb_ps_cv()

Examples

# \donttest{
y <- sim_psy1(150, seed = 1)
res <- radf_sbz(y, minw = 20)
cv <- radf_sbz_cv(y, minw = 20, nboot = 200, seed = 1)
summary(res, cv = cv)
#> 
#> ── Summary (minw = 20, lag = 0) ────────── Wild Bootstrap (SBZ) (nboot = 200) ──
#> 
#> series1 :
#> # A tibble: 3 × 5
#>   stat  tstat  `90`  `95`  `99`
#>   <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf   0.103  1.14  1.56  1.81
#> 2 sadf  3.95   2.13  2.48  3.24
#> 3 gsadf 4.49   2.60  2.92  3.50
#> 
datestamp(res, cv = cv)
#> 
#> ── Datestamp (min_duration = 0) ──────────────────────── Wild Bootstrap (SBZ) ──
#> 
#> series1 :
#>   Start Peak End Duration   Signal Ongoing
#> 1    64   82 102       38 positive   FALSE
#> 2   109  111 113        4 positive   FALSE
#> 3   114  114 115        1 positive   FALSE
#> 
# }