SSR/BIC Bubble Dating (Harvey, Leybourne & Sollis 2017)

dating_hls dates a single bubble episode by fitting four candidate regime-dummy regressions of Delta y_t on y_{t-1} (unit-root-to-end, unit-root-bubble-unit-root, unit-root-bubble-collapse, and unit-root-bubble-collapse-unit-root), each by residual-sum-of-squares minimisation over candidate break fractions, and selects among them by BIC.

Usage

dating_hls(data, trim = 0.05)

# S3 method for class 'dating_hls_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.

trim

Minimum fraction of the (differenced) sample required in every regime (default 0.05, following Harvey, Leybourne & Sollis's own empirical-application choice; their simulations use 0.1).

object

An object of class dating_hls_obj, the output of dating_hls.

Value

An object of class dating_hls_obj: a list with the selected model (model, one of 1:4), its breakpoint date(s) (origination, collapse, recovery – NA for breakpoints the selected model doesn't have), and the BIC value of every candidate model (bic, for inspecting how close the selection was).

Details

Unlike datestamp (threshold-crossing on the recursive BSADF statistic) or dating_pdc (a fixed 3/4-regime structure with sequentially, not jointly, estimated breaks), this jointly searches breakpoints within each of four candidate regime structures and lets BIC pick the structure itself – so it can distinguish "bubble that collapses to a new stationary regime" (Model 3) from "bubble that fully reverts to a unit root" (Model 4) from "bubble ongoing at the sample end" (Model 1), which dating_pdc's fixed regime count cannot. The cost is a genuine joint grid search rather than dating_pdc's sequential one-break- at-a-time scan.

Note

This is an SSR/BIC model-selection dating procedure, not a hypothesis test – it needs no critical values at all.

Returns its own class (not radf_obj), so it does not plug into summary()/\link{datestamp}/tidy/autoplot – 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

Harvey, D. I., Leybourne, S. J., & Sollis, R. (2017). Improving the accuracy of asset price bubble start and end date estimators. Journal of Empirical Finance, 40, 121-138.

See also

dating_pdc for the cheaper sequential-splitting alternative this complements, and datestamp for PSY's original threshold-crossing rule.

Examples

# \donttest{
res <- dating_hls(sim_data$psy1, trim = 0.05)
print(res)
#> 
#> ── dating_hls (n = 100, trim = 0.05) ───────────────────────────────────────────
#> 
#>    series  model  origination  collapse  recovery
#>   series1      4           41        55        62
#> 

# Plot the series with the selected model's breakpoint(s) overlaid
autoplot(res)


# A whole panel at once, faceted one subplot per series
autoplot(dating_hls(sim_data, trim = 0.05))

# }