WLS/Kernel-Volatility Bubble Statistic (SBZ)

radf_sbz computes the WLS (kernel-volatility-weighted) recursive sup-ADF statistic of Harvey, Leybourne & Zu (2019) – supBZ in their own notation – via wls_dfstat_grid() (internal), returning the same shape radf itself does (adf/sadf/gsadf scalars plus the full badf/bsadf recursive paths), so it carries the radf_obj class and the full summary()/ datestamp/tidy/autoplot pipeline works, paired with radf_sbz_cv.

Usage

radf_sbz(data, minw = NULL, kernel = c("gaussian", "uniform"), 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 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. Default: leave-one-out cross-validation over the paper's own search range.

Value

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

Details

Unlike the bundled radf_sbz_union (which combines this with the classic supDF statistic into a bootstrap-calibrated union test), supBZ alone needs no bootstrap to be defined – only to be tested – so it splits into a statistic and a critical-value function the way most of exuber does.

Note

Needs radf_sbz_cv for critical values, not radf_wb_cv or radf_mc_cv – supBZ's own null distribution depends on the WLS weighting, so it needs its own (data-dependent, wild-bootstrap) critical value function, same reasoning as radf()/radf_wb_cv.

Status

References

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

Examples

# \donttest{
# Volatility triples at t = 100, then a strong explosive regime (rho = 1.03)
# from t = 120 to the sample end: supBZ's kernel-volatility weighting trades
# away enough power that sim_psy1()'s default, milder bubble doesn't 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 (minw = 20, lag = 0) ───────────────────────────────────────────────────
#> 
#>        id    adf   sadf  gsadf
#>   series1  4.829  4.829  5.287
#> 
#> [1] gsadf_panel
#> <0 rows> (or 0-length row.names)
#> 

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)

# }