Locally Best Invariant Test for a Bubble (Breitung & Diegel 2025)

lbi_test implements the static locally best invariant (LBI) test of Breitung & Diegel (2025) for a bubble known (or assumed) to span the entire sample: LBI = (y_T - y_1) / (sigma_tilde * sqrt(T - 1)), with sigma_tilde^2 the sample variance of first differences. Heteroskedasticity-robust by construction (the statistic's invariance property does not depend on the exact form of the innovation variance), with a standard normal null distribution – no bootstrap, no simulation, no published table.

Usage

lbi_test(data, level = 0.95)

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.
level: Nominal confidence level for the (one-sided, right-tailed – positive bubbles only) test (default 0.95).

Value

An object of class lbi_test_obj: a list with the test statistic stat, the standard-normal critical value crit, and detected (logical, stat > crit).

Details

Only the static (single, full-sample window) test is implemented. Breitung & Diegel's own headline contribution is a sequential/ exponentially-weighted extension for monitoring an unknown start date, whose exact weighting scheme and boundary constant are not pinned down here and are not implemented.

Note

The critical value is closed-form: the standard normal (qnorm) quantile at level – no bootstrap, no simulation, no table needed.

Status

References

Breitung, J., & Diegel, M. (2025). A locally best invariant sequential test for explosive behavior in the presence of nonstationary volatility. Journal of Time Series Analysis.

Examples

# \donttest{
res <- lbi_test(sim_data$sim_psy1)
#> Warning: Unknown or uninitialised column: `sim_psy1`.
#> Error: unsupported class
print(res)
#> Error: object 'res' not found
# }