Volatility-robust (other routes)

WLS/Kernel-Volatility Bubble Statistic (SBZ)

radf_sbz Replication record →

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

radf_sbz computes the WLS (kernel-volatility-weighted) recursive sup-ADF statistic of Harvey, Leybourne & Zu (2019), called supBZ in their notation, with wls_dfstat_grid() (internal). It returns the same shape as radf: the scalars adf, sadf and gsadf plus the full recursive paths badf and bsadf. The result therefore carries the radf_obj class, and the full summary(), datestamp, tidy and autoplot pipeline works with it when it is paired with radf_sbz_cv.

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 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.

Value

An object of class radf_sbz_obj/radf_obj: a list with adf, sadf and gsadf (one value per series) and badf and bsadf (matrices, one column per series).

Details

The bundled radf_sbz_union combines this statistic with the classic supDF statistic into a bootstrap-calibrated union test. supBZ alone needs a bootstrap only to be tested and not to be defined, so it splits into a statistic and a critical-value function, as most of exuber does.

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 at t = 100, then a strong explosive regime (rho = 1.03)
# runs from t = 120 to the sample end. The kernel-volatility weighting of supBZ
# costs enough power that the milder default bubble of sim_psy1() does not clear it
y <- sim_psy1(n = 200, te = 120, tf = 200, c = 0.03, alpha = 0, seed = 1,
  e = sim_vol_break(199))
res <- radf_sbz(y, minw = 20)
print(res)
#> 
#> ── radf_sbz (minw = 20, kernel = gaussian) ─────────────────────────────────────
#> 
#>    series    adf   sadf  gsadf
#>   series1  4.829  4.829  5.287

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    4.83 0.948  1.65  2.65
#> 2 sadf   4.83 2.24   2.49  3.26
#> 3 gsadf  5.29 2.77   3.00  3.58
tidy(res, cv = cv)
#> # A tibble: 1 × 4
#>   id        adf  sadf gsadf
#>   <fct>   <dbl> <dbl> <dbl>
#> 1 series1  4.83  4.83  5.29
datestamp(res, cv = cv)
#> 
#> ── Datestamp (min_duration = 0) ──────────────────────── Wild Bootstrap (SBZ) ──
#> 
#> series1 :
#>   Start Peak End Duration   Signal Ongoing
#> 1   129  129 130        1 positive   FALSE
#> 2   132  132 133        1 positive   FALSE
#> 3   134  134 135        1 positive   FALSE
#> 4   172  200 200       29 positive    TRUE
autoplot(res, cv = cv)

References

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