Kernel-Purged Heteroskedasticity-Robust PSY Test

radf_kp implements the bootstrap-free heteroskedasticity-robust PSY test of Harvey, Leybourne, Taylor & Zu (2024): it "purges" unconditional heteroskedasticity by cumulating the series' first differences after dividing each by a kernel spot-volatility estimate (eq. 4-5), then runs the ordinary (with-intercept) radf on the purged series.

Usage

radf_kp(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, "gaussian" (default, as in the paper) or "uniform".

h

Bandwidth for the spot-volatility estimator. Default 0.1 * T^(-0.25), the paper's own setting (Table I, Section 6).

Value

A radf_obj, identical in structure to radf's output (so radf_mc_cv, tidy() etc. all apply directly), computed on the volatility-purged series.

Details

Because the purged statistic's null limiting distribution is proven (Theorem 1 / Remark 3.2) to be identical to the standard homoskedastic GSADF null, radf_mc_cv – exuber's existing, already-fast Monte Carlo critical values – applies directly to the result; no new bootstrap or simulation machinery is needed, unlike radf_wb_cv or radf_sbz_cv.

Only the with-intercept variant (\(PSY_\sigma\) in the paper) is implemented. The paper also proposes a without-intercept variant and a union-of-rejections test combining both; these are not implemented here (see the package's enhancement notes for the cost/benefit reasoning).

Note

Returns radf's own output unmodified, so the full summary()/datestamp/tidy/autoplot pipeline works exactly as it does for plain radf() – see vignette("naming-and-analysis", package = "exuber").

Status

References

Harvey, D. I., Leybourne, S. J., Taylor, A. M. R., & Zu, Y. (2024). A new heteroskedasticity-robust test for explosive bubbles. Journal of Time Series Analysis. doi:10.1111/jtsa.12784

See also

radf_mc_cv for this test's (unmodified) critical values, radf_wb_cv for a bootstrap-based alternative, and radf_tt for another bootstrap-free alternative.

Examples

# \donttest{
res <- radf_kp(sim_data, minw = 20)
print(res)
#> 
#> ── radf (minw = 20, lag = 0) ───────────────────────────────────────────────────
#> 
#>      id      adf     sadf   gsadf
#>    psy1  -0.4387   0.1754  1.6743
#>    psy2  -2.4026   0.9183  2.0255
#>   evans  -1.9339  -0.7140  0.4889
#>     div  -2.3185   0.5835  0.8997
#>    blan  -2.4701  -1.4602  0.4523
#> 
#>   gsadf_panel
#>     -0.002803
#> 

# radf_mc_cv() applies unmodified -- see Details
cv <- radf_mc_cv(n = attr(res, "n"), minw = 20)
summary(res, cv = cv)
#> 
#> ── Summary (minw = 20, lag = 0) ────────────────── Monte Carlo (nboot = 1000) ──
#> 
#> psy1 :
#> # A tibble: 3 × 5
#>   stat   tstat   `90`   `95`  `99`
#>   <fct>  <dbl>  <dbl>  <dbl> <dbl>
#> 1 adf   -0.439 -0.488 -0.150 0.408
#> 2 sadf   0.175  0.910  1.26  1.99 
#> 3 gsadf  1.67   1.62   1.90  2.47 
#> 
#> psy2 :
#> # A tibble: 3 × 5
#>   stat   tstat   `90`   `95`  `99`
#>   <fct>  <dbl>  <dbl>  <dbl> <dbl>
#> 1 adf   -2.40  -0.488 -0.150 0.408
#> 2 sadf   0.918  0.910  1.26  1.99 
#> 3 gsadf  2.03   1.62   1.90  2.47 
#> 
#> evans :
#> # A tibble: 3 × 5
#>   stat   tstat   `90`   `95`  `99`
#>   <fct>  <dbl>  <dbl>  <dbl> <dbl>
#> 1 adf   -1.93  -0.488 -0.150 0.408
#> 2 sadf  -0.714  0.910  1.26  1.99 
#> 3 gsadf  0.489  1.62   1.90  2.47 
#> 
#> div :
#> # A tibble: 3 × 5
#>   stat   tstat   `90`   `95`  `99`
#>   <fct>  <dbl>  <dbl>  <dbl> <dbl>
#> 1 adf   -2.32  -0.488 -0.150 0.408
#> 2 sadf   0.584  0.910  1.26  1.99 
#> 3 gsadf  0.900  1.62   1.90  2.47 
#> 
#> blan :
#> # A tibble: 3 × 5
#>   stat   tstat   `90`   `95`  `99`
#>   <fct>  <dbl>  <dbl>  <dbl> <dbl>
#> 1 adf   -2.47  -0.488 -0.150 0.408
#> 2 sadf  -1.46   0.910  1.26  1.99 
#> 3 gsadf  0.452  1.62   1.90  2.47 
#> 
autoplot(res, cv = cv)

# }