Bias-Corrected Bubble Dating (Kejriwal, Nguyen & Perron 2025)

dating_knp(data, trim = 0.05, omit = TRUE, breaks = 2L)

dating_knp dates bubble episodes (origination and collapse) by minimizing a sum of squared residuals that is corrected by omitting a residual. The model has alternating regimes: a unit root, an explosive regime, and a unit root that resumes from a shifted level after an instantaneous collapse, and so on. Plain OLS over this model is provably inconsistent, because the estimate of the origination date converges to the true collapse date and not to the origination date. The default omit = TRUE fixes this by dropping the squared residual at each candidate collapse date from the objective before minimizing.

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.
trim	Minimum fraction of the (differenced) sample required in each regime (default 0.05).
omit	Use the consistency-restoring correction of Kejriwal, Nguyen & Perron (default TRUE). FALSE gives the plain OLS estimator, which is provably inconsistent (their Theorem 1). It is kept mainly to demonstrate the effect of the correction and not for practical dating.
breaks	Number of break dates (the paper's m), two for each bubble. An odd number lets the last bubble run to the end of the sample, and its collapse is then NA.

Value

An object of class dating_knp_obj: a list with origination and collapse (dates) and delta (the fitted explosive AR coefficient). For a single bubble these are named vectors with one value for each series, and for more bubbles they are matrices with one row for each bubble and one column for each series.

Details

breaks = 2 (the default) is the single-bubble model. More breaks use the dynamic-programming algorithm of Kejriwal, Nguyen & Perron, which returns the exact global minimizer of the objective in O(breaks * n^2). As in the paper, the number of breaks is taken as given, for example two for each episode that datestamp finds.

res <- dating_knp(sim_data$psy1, trim = 0.05)
print(res)
#> 
#> ── dating_knp (n = 100, trim = 0.05, omit = TRUE, breaks = 2 ───────────────────
#> 
#>    series  bubble  origination  collapse  delta
#>   series1       1           41        55  0.964
autoplot(res)

# Compare the bias-corrected estimate with the plain (inconsistent) OLS one,
# adding an extra reference line to the output of autoplot()
res_plain <- dating_knp(sim_data$psy1, trim = 0.05, omit = FALSE)
autoplot(res) +
  ggplot2::geom_vline(xintercept = as.numeric(res_plain$origination), linetype = 3)

# Two bubbles
dating_knp(sim_data$psy2, breaks = 4)
#> 
#> ── dating_knp (n = 100, trim = 0.05, omit = TRUE, breaks = 4 ───────────────────
#> 
#>    series  bubble  origination  collapse  delta
#>   series1       1           18        40  1.074
#>   series1       2           59        70  1.066