Reverse-Regression Dating of Crisis Origination and Market Recovery

radf_recovery implements Phillips & Shi (2014)'s reverse- regression dating: reverses the series, runs radf()'s existing bsadf recursion on it, and locates the first up-crossing of a reversal-calibrated critical value boundary (the market recovery date) followed by the next down-crossing (the crisis/collapse origination date in the original series), then maps both back to the original time index.

Usage

radf_recovery(
  data,
  minw = NULL,
  lag = 0,
  nrep = 1000L,
  sig_lvl = 95,
  seed = NULL
)

# S3 method for class 'radf_recovery_obj'
autoplot(object, ...)

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).
lag: A non-negative integer. The lag length of the Augmented Dickey-Fuller regression (default = 0L).
nrep: Number of Monte Carlo replications for radf_recovery_cv's critical value.
sig_lvl: Significance level, one of 90, 95, 99.
seed: Optional seed for the Monte Carlo draws.
object: An object of class radf_recovery_obj, the output of radf_recovery.

Value

An object of class radf_recovery_obj: a list with f_c/f_r (the estimated dates, NA if not identified), detected (logical, whether an up-crossing was found at all), and censored (logical, whether f_c is left-censored by the start of the reverse-time sample).

Details

Two dates are returned per series: f_c, the crisis origination (collapse-onset) date – a reverse-regression-derived alternative to the collapse date datestamp already dates from the forward test – and f_r, the market recovery date, always f_c <= f_r by construction (the down-crossing is searched only after the up-crossing). If no up-crossing is found, neither date is identified (NA, detected = FALSE). If an up-crossing is found but no subsequent down-crossing occurs before the reverse-time sample is exhausted, f_c is NA and censored = TRUE (the crisis origination predates the observed sample).

Note

Returns its own class (not radf_obj), so it does not plug into summary()/\link{datestamp}/tidy/autoplot – prints its own origination/recovery date summary – see vignette("naming-and-analysis", package = "exuber") for the full picture of which functions do and don't fit that pipeline.

Caveats

Validation status (2026-08-10), reported honestly rather than silently: f_r (recovery date) validates well against synthetic collapse-then-recovery data – bias in the same range the paper's own Monte Carlo reports (a few observations early). f_c (crisis origination date) shows a materially larger residual bias in Monte Carlo checks, and the empirical false-detection rate under a pure random-walk null (n=100, minw=20, 95\ than comparable forward-test numbers elsewhere in this package. One real synthetic-DGP artifact (a level-jump at a regime boundary producing a spurious spike) was found and fixed during validation, but the residual f_c bias/false-detection elevation was not fully resolved – plausibly genuine finite-sample noise in the paper's own literal first-down-crossing rule (eq. 9's inf has no persistence requirement, so a transient dip below the boundary is enough to trigger a premature f_c), but this has not been ruled out against a subtler implementation issue. Treat f_c and the overall detection rate as exploratory pending further validation; see docs/enhancements/dating-and-root-inference.md for the full numbers. The same short pointer is emitted as a message when this function is called (see suppressMessages to silence it) and stored as attr(x, "caveat") on the returned object.

References

Phillips, P. C. B., & Shi, S. (2014). Financial Bubble Implosion and Reverse Regression. Cowles Foundation Discussion Paper No. 1967, Yale University. Published in Econometric Theory.

Examples

# \donttest{
# sim_ps1()'s own expansion -> bubble -> collapse -> recovery DGP
y <- sim_ps1(n = 100, seed = 1)
res <- radf_recovery(y, minw = 15, nrep = 200, seed = 1)
#> Experimental. f_c and the overall false-detection rate are exploratory pending further validation; see ?radf_recovery, Caveats section.
print(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
#> 

# Plot the series with the estimated collapse (f_c) / recovery (f_r) points
autoplot(res)

# }