Sequential Sample-Splitting Bubble Dating (PDC/KS)

dating_pdc dates a single bubble episode using the sequential sample-splitting method of Pang, Du & Chong (2021) and its 4-regime extension by Kurozumi & Skrobotov (2023): a fixed regime structure (unit-root, explosive, stationary-collapse, and optionally a final unit-root recovery regime) whose breakpoints are estimated one at a time, each a closed-form residual-sum-of-squares minimisation over a no-intercept AR(1) model, in \(O(T)\) via cumulative sums.

Usage

dating_pdc(
  data,
  regimes = 3L,
  trim = 0.05,
  type = c("ols", "wls"),
  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.
regimes: Either 3 (PDC: unit-root, explosive, stationary collapse) or 4 (KS: adds a final unit-root recovery regime after the collapse).
trim: Minimum fraction of the (differenced) sample required on either side of each breakpoint search (default 0.05, as in KS's empirical application; PDC use 0.05-0.1 in their simulations).
type: "ols" (default) for the plain homoskedastic estimator, or "wls" for Kurozumi & Skrobotov (2023)'s volatility-corrected two-step estimator.
kernel: Kernel for the spot-volatility estimator when type = "wls", "gaussian" (default) or "uniform". Ignored when type = "ols".
h: Bandwidth for the spot-volatility estimator when type = "wls". Default: leave-one-out cross-validation. Ignored when type = "ols".

Value

An object of class dating_pdc_obj (a data.frame with one row per series and columns origination, collapse, and (if regimes = 4) recovery, giving the estimated break dates (or observation indices, if no date index is available); it has its own print() and autoplot() methods.

Details

Unlike datestamp (which finds where the recursive BSADF statistic crosses a critical value), this fits an explicit regime-switching model directly to the series; it needs no critical values at all. PDC prove the collapse date is identified first – its effect on the residual sum of squares dominates the origination date's – which is what licenses estimating the breaks sequentially rather than jointly (unlike Harvey, Leybourne & Sollis's (2017) BIC-selected, jointly-fit alternative, which is not implemented here; see the package's enhancement notes for the cost/benefit reasoning).

type = "wls" adds Kurozumi & Skrobotov (2023)'s time-varying- volatility correction: fit the plain ("ols") model first, collect its fitted piecewise-regime residuals, smooth their square nonparametrically (the same Nadaraya-Watson kernel/leave-one-out bandwidth estimator exuber already uses for radf_sbz_cv/radf_kp), and re-run the same sequential break search with each squared term weighted by the inverse of the estimated spot variance. This needs no new critical-value theory – like the OLS version, it is point estimation, not a threshold-crossing test.

Note

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

Status

References

Pang, T., Du, L., & Chong, T. T. L. (2021). Estimating multiple breaks in the bubble regime with SSR minimization. Journal of Management Science and Engineering.

Kurozumi, E., & Skrobotov, A. (2023). Bubble dating: a sequential testing approach.

Kurozumi, E., & Skrobotov, A. (2023). Improving the accuracy of bubble date estimators under time-varying volatility. arXiv:2306.02977.

Examples

# \donttest{
# sim_ps1()'s unit-root -> explosive -> collapse -> recovery DGP is exactly
# the regime structure dating_pdc() fits (true breaks at 40, 60, 70)
y <- sim_ps1(n = 100, seed = 1)
res <- dating_pdc(y, regimes = 3L, trim = 0.05)
print(res)
#> 
#> ── dating_pdc (n = 100, regimes = 3, type = ols) ───────────────────────────────
#> 
#>    series  origination  collapse
#>   series1           38        59
#> 
autoplot(res)


# 4-regime extension, adding a post-collapse recovery breakpoint
res4 <- dating_pdc(y, regimes = 4L, trim = 0.05)
autoplot(res4)


# Volatility-weighted (WLS) variant, robust to time-varying volatility
y_vol <- sim_ps1(n = 100, seed = 1, e = sim_vol_break(99))
autoplot(dating_pdc(y_vol, type = "wls"))

# }