Wild Bootstrap Critical Values (Phillips & Shi 2020)

radf_wb_ps_cv generates critical values for the recursive unit root tests with the wild bootstrap of Phillips & Shi (2020). The scheme fits a null AR model and resamples its residuals, and it is asymptotically robust to non-stationary volatility. radf_wb_ps_distr computes the distribution. In contrast to the non-parametric multiplier bootstrap of Harvey et al. (2016) in radf_wb_cv, this version supports a training-window boundary (tb), which is what monitor uses it for.

Usage

radf_wb_ps_cv(
  data,
  minw = NULL,
  nboot = 500L,
  adflag = 0,
  type = c("fixed", "aic", "bic"),
  tb = NULL,
  seed = NULL
)

radf_wb_ps_distr(
  data,
  minw = NULL,
  nboot = 500L,
  adflag = 0,
  type = c("fixed", "aic", "bic"),
  tb = NULL,
  seed = NULL
)

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.

minw

A positive integer. The minimum window size (default = \((0.01 + 1.8/\sqrt{T})T\), where T denotes the sample size).

nboot

A positive integer. Number of bootstraps (default = 500L).

adflag

A positive integer. Number of lags when type is "fixed" or number of max lags when type is either "aic" or "bic".

type

Character. "fixed" for fixed lag, "aic" or "bic" for automatic lag selection according to the criterion.

tb

A positive integer. The simulated sample size.

seed

An object specifying if and how the random number generator (rng) should be initialized. It is either NULL or an integer, which is passed to set.seed before the simulation. If you set it, the value is saved as the "seed" attribute of the returned value. The default, NULL, leaves the state of the rng unchanged and returns .Random.seed as the "seed" attribute. Results are reproducible across the parallel and the non-parallel option when you use the same seed.

Value

For radf_wb_ps_cv, a list with the critical values for the ADF, BADF, BSADF and GSADF tests. For radf_wb_ps_distr, a list with the ADF, SADF and GSADF distributions.

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.

Phillips, P. C. B., Shi, S., & Yu, J. (2015). Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500. International Economic Review, 56(4), 1043-1078. doi:10.1111/iere.12132

See also

radf_wb_cv for the Harvey et al. (2016) wild bootstrap, radf_mc_cv for Monte Carlo critical values and radf_sb_cv for sieve bootstrap critical values.

Other critical values: radf_common_cv(), radf_mc_cv(), radf_recovery_cv(), radf_sb_cv(), radf_sbz_cv(), radf_sign_cv(), radf_sign_dm_cv(), radf_tt_cv(), radf_wb_cv()

Examples

# \donttest{
# Default minimum window
wb <- radf_wb_ps_cv(sim_data)

tidy(wb)
#> # A tibble: 15 × 5
#>    id    sig       adf  sadf gsadf
#>    <fct> <fct>   <dbl> <dbl> <dbl>
#>  1 psy1  90    -0.423   1.14  2.13
#>  2 psy2  90    -0.426   1.44  2.33
#>  3 evans 90    -0.431   1.42  2.67
#>  4 div   90    -0.218   1.10  1.90
#>  5 blan  90    -0.493   1.25  2.27
#>  6 psy1  95    -0.0690  1.59  2.49
#>  7 psy2  95    -0.151   2.02  3.01
#>  8 evans 95    -0.109   2.02  3.27
#>  9 div   95     0.119   1.54  2.38
#> 10 blan  95    -0.168   1.64  2.73
#> 11 psy1  99     0.788   2.81  3.86
#> 12 psy2  99     0.735   3.38  4.77
#> 13 evans 99     0.504   3.29  5.21
#> 14 div   99     0.819   2.05  3.25
#> 15 blan  99     0.522   2.40  3.92

# Change the minimum window and the number of bootstraps
wb2 <- radf_wb_ps_cv(sim_data, nboot = 600, minw = 20)

tidy(wb2)
#> # A tibble: 15 × 5
#>    id    sig         adf  sadf gsadf
#>    <fct> <fct>     <dbl> <dbl> <dbl>
#>  1 psy1  90    -0.382     1.26  2.08
#>  2 psy2  90    -0.398     1.40  2.34
#>  3 evans 90    -0.399     1.32  2.63
#>  4 div   90    -0.365     1.16  2.01
#>  5 blan  90    -0.337     1.45  2.35
#>  6 psy1  95    -0.124     1.75  2.51
#>  7 psy2  95    -0.0329    1.78  2.94
#>  8 evans 95     0.0270    1.87  3.19
#>  9 div   95    -0.0363    1.54  2.46
#> 10 blan  95    -0.000135  1.91  3.04
#> 11 psy1  99     0.563     2.51  3.16
#> 12 psy2  99     0.453     2.84  4.67
#> 13 evans 99     0.729     3.17  4.54
#> 14 div   99     0.455     2.14  3.56
#> 15 blan  99     0.967     2.94  4.01

# Simulate distribution
wdist <- radf_wb_ps_distr(sim_data)

autoplot(wdist)


# Apply the critical values to actual data
rsim_data <- radf(sim_data, minw = 20)
autoplot(rsim_data, cv = wb2)

# }