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Wild Bootstrap Critical Values

Source: R/radf_wb.R
radf_wb_cv.Rd

radf_wb_cv performs the Harvey et al. (2016) wild bootstrap re-sampling scheme, which is asymptotically robust to non-stationary volatility, to generate critical values for the recursive unit root tests. radf_wb_distr computes the distribution.

Usage

radf_wb_cv(
  data,
  minw = NULL,
  nboot = 500L,
  dist_rad = FALSE,
  dist_skew = FALSE,
  seed = NULL
)

radf_wb_distr(
  data,
  minw = NULL,
  nboot = 500L,
  dist_rad = FALSE,
  dist_skew = FALSE,
  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 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).

nboot

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

dist_rad

Logical. If TRUE then the Rademacher distribution will be used.

dist_skew

Logical. If TRUE, use Hafner (2020)'s fixed right-skewed multiplier distribution instead of the (default) standard normal or (dist_rad = TRUE) Rademacher one – appropriate when the series' return distribution is itself notably right-skewed (e.g. cryptocurrency returns, the paper's own application). At most one of dist_rad and dist_skew may be TRUE.

seed

An object specifying if and how the random number generator (rng) should be initialized. Either NULL or an integer will be used in a call to set.seed before simulation. If set, the value is saved as "seed" attribute of the returned value. The default, NULL, will not change rng state, and return .Random.seed as the "seed" attribute. Results are reproducible across the parallel and non-parallel option when the same seed is used.

Value

For radf_wb_cv a list that contains the critical values for the ADF, BADF, BSADF and GSADF tests. For radf_wb_distr a list that contains the ADF, SADF and GSADF distributions.

Details

This approach involves applying a wild bootstrap re-sampling scheme to construct the bootstrap analogue of the Phillips et al. (2015) test which is asymptotically robust to non-stationary volatility.

References

Harvey, D. I., Leybourne, S. J., Sollis, R., & Taylor, A. M. R. (2016). Tests for explosive financial bubbles in the presence of non-stationary volatility. Journal of Empirical Finance, 38(Part B), 548-574.

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.

Hafner, C. M. (2020). Testing for bubbles in cryptocurrencies with time-varying volatility. Journal of Financial Econometrics, 18(2), 233-249.

See also

radf_mc_cv for Monte Carlo critical values and radf_sb_cv for sieve bootstrap critical values.

Examples

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

tidy(wb)
#> # A tibble: 15 × 5
#>    id    sig        adf   sadf gsadf
#>    <fct> <fct>    <dbl>  <dbl> <dbl>
#>  1 psy1  90    -0.543    1.53   2.71
#>  2 psy2  90    -0.622    3.07   4.06
#>  3 evans 90    -0.497    5.38   7.05
#>  4 div   90    -0.473    0.848  1.72
#>  5 blan  90    -0.211    2.87   6.25
#>  6 psy1  95    -0.342    2.16   3.39
#>  7 psy2  95    -0.507    3.81   4.89
#>  8 evans 95    -0.324    6.77   9.28
#>  9 div   95    -0.145    1.14   2.06
#> 10 blan  95    -0.00843  4.08   7.37
#> 11 psy1  99     0.0446   3.16   4.75
#> 12 psy2  99    -0.294    5.29   6.15
#> 13 evans 99    -0.0223  10.4   13.6 
#> 14 div   99     0.227    1.94   2.56
#> 15 blan  99     0.389    7.62  10.8 

# Change the minimum window and the number of bootstraps
wb2 <- radf_wb_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    -0.555   1.48   2.74
#>  2 psy2  90    -0.665   2.72   3.78
#>  3 evans 90    -0.547   5.06   8.40
#>  4 div   90    -0.436   0.905  1.76
#>  5 blan  90    -0.247   2.86   5.92
#>  6 psy1  95    -0.430   2.03   3.19
#>  7 psy2  95    -0.502   3.34   4.55
#>  8 evans 95    -0.346   7.54  10.5 
#>  9 div   95    -0.0561  1.21   1.99
#> 10 blan  95     0.0278  4.31   7.65
#> 11 psy1  99    -0.0550  3.09   4.56
#> 12 psy2  99    -0.171   4.62   5.60
#> 13 evans 99    -0.0145 11.7   14.0 
#> 14 div   99     0.486   1.93   2.50
#> 15 blan  99     0.605   6.68  12.4 

# Simulate distribution
wdist <- radf_wb_distr(sim_data)

autoplot(wdist)

# }