Recursively Demeaned Sign-Based Bubble Test (s-bar-PWY / s-bar-PSY)

radf_sign_dm computes Harvey, Leybourne & Zu (2020)'s second sign-based analogue of the recursive right-tailed unit root test, denoted \(\bar{s}PWY\)/\(\bar{s}PSY\) in the paper: the same construction as radf_sign, but built on a recursively (expanding-window) demeaned cumulated-sign series, Ctilde_t = sum_{i=2}^{t} (sign(diff(y)_i) - mean(sign(diff(y)_{2:i}))), rather than the raw cumulated sign radf_sign uses.

Usage

radf_sign_dm(data, minw = 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).

Value

An object of class radf_sign_dm_obj/radf_obj: the same adf/badf/sadf/bsadf/gsadf list as radf; pair with radf_sign_dm_cv.

Details

Harvey, Leybourne, Tatlow & Zu (2025) show this statistic shares radf_sign's asymptotic level-shift robustness (see that function's Level-shift robustness section) without requiring Assumption 2 of the underlying HLZ (2020) theory (that the innovations' median is zero) – a strictly weaker requirement than radf_sign needs for its own invariance result. Their finite -sample simulations also find the recursive demeaning tends to further reduce size distortion under level shifts relative to radf_sign, though both are asymptotically level-shift robust under the same condition.

Note

Needs radf_sign_dm_cv for critical values (not radf_sign_cv, which is calibrated to the non-demeaned radf_sign statistic instead) – pivotal like radf_sign, so no per-dataset bootstrap is needed.

Carries the radf_obj class and, as of 2026-08-18, its full summary()/datestamp/tidy/autoplot pipeline works, the same fix as radf_sign – radf_sign_dm_cv() now computes badf_cv/bsadf_cv too, not just the three scalar critical values. See vignette("naming-and-analysis", package = "exuber").

Status

References

Harvey, D. I., Leybourne, S. J., & Zu, Y. (2020). Sign-based unit root tests for explosive financial bubbles in the presence of deterministically time-varying volatility. Econometric Theory, 36(1), 122-169.

Harvey, D. I., Leybourne, S. J., Tatlow, D., & Zu, Y. (2025). Unit root tests for explosive financial bubbles in the presence of deterministic level shifts. Oxford Bulletin of Economics and Statistics, 87(5), 879-901. doi:10.1111/obes.12668

See also

radf_sign_dm_cv for critical values, and radf_sign for the non-demeaned sign-based analogue.

Other volatility-robust tests: radf_kp(), radf_sbz(), radf_sbz_union(), radf_sign(), radf_tt(), ssu_test()

Examples

# \donttest{
# Volatility triples half-way through the sample: the non-stationary-volatility
# case this test is built for (plain radf() over-rejects here)
y <- sim_psy1(n = 200, seed = 1, e = sim_vol_break(199))
res <- radf_sign_dm(y, minw = 20)
print(res)
#> 
#> ── radf_sign_dm (minw = 20) ────────────────────────────────────────────────────
#> 
#>    series       adf   sadf  gsadf
#>   series1  -0.03298  2.492  6.081
#> 

cv <- radf_sign_dm_cv(n = 200, minw = 20)
summary(res, cv = cv)
#> 
#> ── Summary (minw = 20, lag = 0) ───── Sign-Based MC (demeaned) (nboot = 2000) ──
#> 
#> series1 :
#> # A tibble: 3 × 5
#>   stat    tstat  `90`  `95`  `99`
#>   <fct>   <dbl> <dbl> <dbl> <dbl>
#> 1 adf   -0.0330 0.853  1.28  2.09
#> 2 sadf   2.49   2.45   2.80  3.46
#> 3 gsadf  6.08   3.32   3.66  4.58
#> 
tidy(res, cv = cv)
#> # A tibble: 1 × 4
#>   id          adf  sadf gsadf
#>   <fct>     <dbl> <dbl> <dbl>
#> 1 series1 -0.0330  2.49  6.08
datestamp(res, cv = cv)
#> 
#> ── Datestamp (min_duration = 0) ──────────────────── Sign-Based MC (demeaned) ──
#> 
#> series1 :
#>   Start Peak End Duration   Signal Ongoing
#> 1    91  103 115       24 positive   FALSE
#> 2   156  157 158        2 negative   FALSE
#> 3   159  160 161        2 negative   FALSE
#> 
autoplot(res, cv = cv)

# }