Skip to contents

SBZ Weighted Least Squares Bubble Test with Union-of-Rejections

Source: R/radf_sbz.R
radf_sbz_cv.Rd

radf_sbz_cv performs the HLST (2016) wild bootstrap – the same algorithm as radf_wb_cv – jointly on the classic sup-ADF statistic (supDF, i.e. radf()'s sadf) and the WLS/kernel-volatility statistic supBZ of Harvey, Leybourne & Zu (2019), and combines them into the paper's union-of-rejections statistic U. supBZ can have substantially higher power than supDF under many time-varying-volatility patterns, at the cost of lower power under others (e.g. upward volatility trends); U is designed to capture whichever of the two is more powerful for a given series.

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 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).

nboot

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

kernel

Kernel for the spot-volatility estimator (eq. 6), "gaussian" (default, as in the paper) or "uniform".

h

Bandwidth for the spot-volatility estimator. Default: leave-one-out cross-validation over the paper's own search range.

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.seed before 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.

Value

A list with bootstrap p-values (p_supDF, p_supBZ, p_U) and critical values (supDF_cv, supBZ_cv, U_cv) for each series.

Note

This function bundles the statistic and its critical values in a single call – there is no separate un-cv'd statistic function and no other critical-value function to pair it with, unlike radf()/ radf_wb_cv().

Status

[Experimental]

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_wb_cv for the underlying (supDF-only) wild bootstrap, and radf_tt for a bootstrap-free heteroskedasticity-robust alternative.

Examples

# \donttest{
res <- radf_sbz_cv(sim_data, nboot = 200)
print(res)
#> 
#> ── radf_sbz (minw = 19, nboot = 200) ───────────────────────────────────────────
#> 
#>   series  supDF   supBZ      U  p_supDF  p_supBZ    p_U
#>     psy1  1.946  0.2802  1.946    0.045    0.580  0.070
#>     psy2  7.880  1.5349  7.880    0.000    0.175  0.000
#>    evans  5.283  1.9138  5.283    0.085    0.285  0.120
#>      div  1.113  2.2607  1.336    0.100    0.080  0.110
#>     blan  3.930  1.4008  3.930    0.060    0.235  0.085
#> 
# }