Experimental Methods: radf_recovery() and datestamp(option = 'svadf')

library(exuber)

What “experimental” means here

Most methods in exuber implement the procedure of a peer-reviewed paper and pass the package’s standard validation. That validation consists of a formula-exact check against a brute-force reimplementation, a lookup against published tables, a Monte Carlo check of size, and a check of power against a true alternative. radf_recovery() and datestamp(option = "svadf") went through the same validation and both give useful results, but each has one disclosed gap that keeps it below the standard. For that reason they print and emit a caveat message when called. Treat their output as a guide to where episodes lie, and do not assume it is as well calibrated as the rest of the package.

radf_recovery(): dating a collapse and a recovery

This function uses the reverse-regression idea of Phillips & Shi (2014). We reverse the series in time, run the BSADF recursion that radf() already computes, and map the crossing dates back to the original time axis. In the reversed series a collapse followed by a recovery turns the collapse into an explosive regime and the recovery into the end of that regime, so the forward machinery run backwards dates both.

# sim_ps1(): unit root -> explosive (40-60) -> collapse (61-70) -> recovery (71+)
y <- sim_ps1(n = 100, seed = 2)
res <- radf_recovery(y, minw = 15, nrep = 200, seed = 1)
res
#> 
#> ── radf_recovery (n = 100, minw = 15, level = 95%) ─────────────────────────────
#> 
#> ℹ Experimental. f_c and the overall false-detection rate are exploratory pending further validation; see ?radf_recovery, Caveats section.
#> 
#>    series  f_c  f_r  detected  censored
#>   series1   57   67      TRUE     FALSE

The estimate f_c (crisis onset, 57) falls just before the true collapse start (61). The estimate f_r (recovery, 67) falls after it, inside the collapse regime and before the true recovery date (70). The two dates come out in the right order by construction, because the down-crossing search only starts at the up-crossing. The disclosed gap is that f_c and the overall false-detection rate are exploratory until they are validated further (see the Caveats section of ?radf_recovery). The ordering of the dates is reliable, but the calibration of false alarms is not yet.

datestamp(option = "svadf"): a preprint

This option implements Sarkar & Wells (2026), an arXiv preprint that has not been peer reviewed. Every other paper implemented in the package has been, so the evidence behind this method is weaker. Its statistic is the badf sequence that radf() already computes, compared against two closed-form thresholds that depend only on the sample size and come from the applied methodology of the paper. No new estimation code was needed, so we added it as an option of datestamp() and not as a separate function, even though it is a preprint.

res <- radf(sim_data, lag = 0)
datestamp(res, option = "svadf", min_duration = psy_ds(nrow(sim_data)))
#> 
#> ── Datestamp (min_duration = 5) ──────────────── SV-ADF (Sarkar & Wells 2026) ──
#> 
#> ℹ Experimental. Sarkar & Wells (2026) is a non-peer-reviewed preprint; see ?datestamp, Caveats section.
#> 
#> psy1 :
#>   Start Peak End Duration   Signal Ongoing
#> 1    48   48  49        1 positive   FALSE
#> 
#> psy2 :
#>   Start Peak End Duration   Signal Ongoing
#> 1    23   23  24        1 positive   FALSE

psy1 and psy2 receive clear origination and collapse dates, while evans, div and blan never cross the threshold in this panel. We report this mixed result as it came out.

Using them responsibly

Both methods are worth using. The date ordering from radf_recovery() and the point statistic from datestamp(option = "svadf") are reliable. Neither should be the only basis for a claim about false-alarm rates or exact calibration, though. When that matters, prefer radf() and datestamp(), or one of the peer-reviewed alternatives in vignette("alternative-tests") and vignette("dating-methods"). Treat these two methods as a second opinion until their caveats are resolved. The caveats are tracked in docs/dating-and-root-inference.md and volatility-robustness.md.