Common-Bubble Detection via PCA + PSY

radf_common tests for a bubble common to a panel of series (Chen, Phillips & Shi, 2023): it extracts the panel's first principal component and runs the ordinary radf test on it – and every downstream method (tidy(), autoplot(), datestamp(), ...) works on it for free, since the output is an ordinary radf_obj.

Usage

radf_common(data, minw = NULL, r = 1)

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).
r: Number of principal components to extract (default 1, the paper's own recommendation: "sufficient... for the purpose of bubble identification"). Only the first is used for detection; the rest are returned for inspection via the "prcomp" attribute.

Value

A radf_obj (see radf) computed on the panel's first principal component, with the fitted prcomp object attached as an attribute (attr(x, "prcomp")).

Details

The paper's own Theorem 4.3 claims the resulting statistic's null limiting distribution is asymptotically identical to the standard PSY/GSADF one, which would let radf_mc_cv apply directly. An independent validation found this identity does not hold at practical panel widths N: the true critical value is more than double radf_mc_cv's at N = 100, and the gap grows as N increases – PCA on a panel of merely independent (non-cointegrated) I(1) series does not behave like a single random walk once there are more series to draw transient co-movement from. Use radf_common_cv for critical values, not radf_mc_cv, which has no dependence on panel width and is badly undersized here once N grows past a handful of series.

Status

References

Chen, Y., Phillips, P. C. B., & Shi, S. (2023). Common Bubble Detection in Large Dimensional Financial Systems. Journal of Financial Econometrics, 21(4), 989-1063.

Examples

# \donttest{
res <- radf_common(sim_data, minw = 20)
print(res)
#> 
#> ── radf (minw = 20, lag = 0) ───────────────────────────────────────────────────
#> 
#>        id     adf   sadf  gsadf
#>   series1  -2.734  7.145  7.145
#> 
#>   gsadf_panel
#>         7.145
#> 

# radf_common_cv() is needed here -- NOT radf_mc_cv(), see Details
cv <- radf_common_cv(n = 100, N = ncol(sim_data), minw = 20)
summary(res, cv = cv)
#> 
#> ── Summary (minw = 20, lag = 0) ─────────────────── Monte Carlo (nrep = 1000) ──
#> 
#> series1 :
#> # A tibble: 3 × 5
#>   stat  tstat  `90`  `95`  `99`
#>   <fct> <dbl> <dbl> <dbl> <dbl>
#> 1 adf   -2.73 0.300 0.620  1.40
#> 2 sadf   7.15 1.81  2.13   2.68
#> 3 gsadf  7.15 2.32  2.63   3.25
#> 
# }