Sign-Based Bubble Test (sPWY / sPSY)

radf_sign(data, minw = NULL)

radf_sign computes the sign-based variant of the recursive right-tailed unit root test of Harvey, Leybourne & Zu (2020). Instead of applying the (double-)supremum ADF test to the series itself, it applies it to the cumulated sign of the first differences, C_t = sum(sign(diff(y))). The sign() function removes all information about magnitudes, so the recursive DF statistic of C_t is exactly invariant to the pattern of volatility in the innovations, even when volatility changes over time. Unlike radf, the test needs no wild bootstrap to control its size under heteroskedasticity. The critical values in radf_sign_cv are pivotal, so they are computed once and not for each dataset.

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).

Value

An object of class radf_sign_obj/radf_obj. It is the same adf/badf/sadf/bsadf/gsadf list as for radf, computed on the sign-transformed series, and it pairs with radf_sign_cv.

Details

The price of this invariance is power. The paper finds that the sign-based test outperforms the standard PSY test for many specifications of time-varying volatility and bubbles, but not for all of them, and the standard test can still win in some. The strategy that the paper recommends in practice is a bootstrap-based union of rejections that combines both tests. We have not implemented it (see the package's enhancement notes for the cost and benefit considerations), and this function provides the standalone sign-based test only. sadf is the single-supremum sPWY statistic (r1 = 0 fixed), and gsadf is the double-supremum sPSY statistic.

# Volatility triples half-way through the sample. This is the case of
# non-stationary volatility that this test is built for, and plain radf()
# over-rejects here
y <- sim_psy1(n = 200, seed = 1, e = sim_vol_break(199))
res <- radf_sign(y, minw = 20)
print(res)
#> 
#> ── radf_sign (minw = 20) ───────────────────────────────────────────────────────
#> 
#>    series      adf   sadf  gsadf
#>   series1  -0.2933  4.468  8.879

cv <- radf_sign_cv(n = 200, minw = 20)
summary(res, cv = cv)
#> 
#> ── Summary (minw = 20, lag = 0) ──────────────── Sign-Based MC (nboot = 2000) ──
#> 
#> series1 :
#> # A tibble: 3 × 5
#>   stat   tstat  `90`  `95`  `99`
#>   <fct>  <dbl> <dbl> <dbl> <dbl>
#> 1 adf   -0.293 0.855  1.32  2.06
#> 2 sadf   4.47  2.34   2.70  3.43
#> 3 gsadf  8.88  3.51   3.91  4.92
tidy(res, cv = cv)
#> # A tibble: 1 × 4
#>   id         adf  sadf gsadf
#>   <fct>    <dbl> <dbl> <dbl>
#> 1 series1 -0.293  4.47  8.88
datestamp(res, cv = cv)
#> 
#> ── Datestamp (min_duration = 0) ─────────────────────────────── Sign-Based MC ──
#> 
#> series1 :
#>   Start Peak End Duration   Signal Ongoing
#> 1    84   84  85        1 positive   FALSE
#> 2    87  103 122       35 positive   FALSE
#> 3   123  123 124        1 positive   FALSE
autoplot(res, cv = cv)