Real-Time Monitoring for Explosive Bubbles

radf_monitor implements real-time monitoring: fix a training window [1, T*] assumed free of exuberance, calibrate a critical value on it, then compare the running recursive statistic at each subsequent point T*+1, ..., T against that fixed boundary, flagging the first date it is breached.

Usage

radf_monitor(
  data,
  r_star = 0.5,
  minw = NULL,
  nboot = 500L,
  level = 0.95,
  adflag = 0,
  type = c("fixed", "aic", "bic"),
  seed = NULL,
  boundary = c("bootstrap", "kurozumi", "fluc"),
  s0 = 0
)

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.
r_star: The end of the training window: a fraction in (0, 1) of the sample (default 0.5), or an integer observation count if >= 1.
minw: A positive integer. The minimum window size (default = \((0.01 + 1.8/\sqrt(T))T\), where T denotes the sample size).
nboot: Number of wild bootstrap replications for the training critical value. Ignored unless boundary = "bootstrap".
level: Nominal confidence level for the monitoring boundary (default 0.95). When boundary is "kurozumi" or "fluc", must be one of 0.90, 0.95, 0.99.
adflag, type: Passed to radf_wb_cv2 (lag length / selection for the wild bootstrap DGP). Ignored unless boundary = "bootstrap".
seed: Optional seed for the bootstrap draws. Ignored unless boundary = "bootstrap".
boundary: "bootstrap" (default, Phillips & Shi 2020), "kurozumi" (Kurozumi 2020's closed-form SADF/GSADF boundary), or "fluc" (Homm & Breitung 2012's FLUC boundary).
s0: Kurozumi (2020)'s window-start range as a fraction of the training length, only used when boundary = "kurozumi". 0 (default) is the SADF case (window start fixed at 1); 0.4 or 0.8 switches to the GSADF_{s0} case (window start ranges over [1, floor(T* * s0)]), the only two values his boundary function's scaling constants are tabulated for.

Value

An object of class radf_monitor_obj: a list with the full-sample statistic path (stat – bsadf for boundary = "bootstrap", badf for "kurozumi"/ "fluc"), the calibrated boundary (one flat value per series), the training window length T_star, and alarm/alarm_date (the first monitoring-period observation/date at which stat breaches the boundary, NA if never).

Details

boundary = "bootstrap" (default) implements Phillips & Shi (2020): the boundary is a wild-bootstrap quantile of the GSADF-type statistic (radf_wb_cv2, its tb parameter), compared against radf()'s bsadf sequence. Deliberately calibrates on the training window only (data[1:T*]), not the full series: radf_wb_cv2's underlying null-model fit (adf_res()) uses whatever data it is given in full, with no internal truncation to tb – passing post-T* (possibly explosive) data to it directly would leak future information into the null calibration.

boundary = "kurozumi" implements Kurozumi (2020)'s closed-form alternative: no bootstrap at all, just a published constant (his Table 1) compared against radf()'s badf sequence (his SADF(k) detector – the s0 = 0, fixed-start-at-1 case, the default). Setting s0 to 0.4 or 0.8 instead switches to his GSADF_{s0}(k) generalization: the window start is allowed to range over [1, floor(T* * s0)] rather than being fixed at 1, compared against his k-varying (not constant) boundary function and its own published scaling constant. level must be one of 0.90, 0.95, or 0.99 (the levels his table tabulates).

boundary = "fluc" implements Homm & Breitung (2012)'s FLUC detector: their DF_{t/n} is likewise exactly radf()'s badf sequence, compared against a published constant from their Table 7 (no detrending case) rather than a simulated one. level must be one of 0.90, 0.95, 0.99.

Status

References

Phillips, P. C., & Shi, S. (2020). Real time monitoring of asset markets: Bubbles and crises. In Handbook of Statistics (Vol. 42, pp. 61-80). Elsevier.

Kurozumi, E. (2020). Asymptotic properties of bubble monitoring tests. Econometric Reviews, 39(5), 510-538.

Homm, U., & Breitung, J. (2012). Testing for speculative bubbles in stock markets: A comparison of alternative methods. Journal of Financial Econometrics, 10(1), 198-231.

Examples

# \donttest{
# Default: Phillips & Shi (2020) wild bootstrap boundary
mon <- radf_monitor(sim_data, r_star = 0.5, nboot = 200)
print(mon)
#> 
#> ── radf_monitor (T* = 50 / 100, minw = 19, level = 95%, boundary = bootstrap) ──
#> 
#>   series  boundary  alarm  alarm_date
#>     psy1     1.852     51          51
#>     psy2     1.867     65          65
#>    evans     2.565     67          67
#>      div     1.786     NA        <NA>
#>     blan     2.459     85          85
#> 

# Kurozumi (2020) closed-form boundary -- no bootstrap needed
mon_kz <- radf_monitor(sim_data, r_star = 0.5, boundary = "kurozumi")
print(mon_kz)
#> 
#> ── radf_monitor (T* = 50 / 100, minw = 19, level = 95%, boundary = kurozumi) ───
#> 
#>   series  boundary  alarm  alarm_date
#>     psy1     1.038     51          51
#>     psy2     1.038     NA        <NA>
#>    evans     1.038     NA        <NA>
#>      div     1.038     NA        <NA>
#>     blan     1.038     NA        <NA>
#> 
# }