Wild Bootstrap Critical Values

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.

Examples

# \donttest{
# Volatility triples half-way through the sample: the non-stationary-volatility
# case the wild bootstrap is built for (plain radf_mc_cv() over-rejects here)
y <- sim_psy1(n = 200, seed = 1, e = sim_vol_break(199))
# Default minimum window
wb <- radf_wb_cv(y)

tidy(wb)
#> # A tibble: 3 × 5
#>   id      sig      adf  sadf gsadf
#>   <fct>   <fct>  <dbl> <dbl> <dbl>
#> 1 series1 90    -0.135  3.82  4.32
#> 2 series1 95     0.276  4.81  5.22
#> 3 series1 99     1.16   6.57  7.24

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

tidy(wb2)
#> # A tibble: 3 × 5
#>   id      sig       adf  sadf gsadf
#>   <fct>   <fct>   <dbl> <dbl> <dbl>
#> 1 series1 90    -0.209   3.98  4.52
#> 2 series1 95     0.0593  5.02  5.37
#> 3 series1 99     0.913   7.01  7.39

# Simulate distribution
wdist <- radf_wb_distr(y)

autoplot(wdist)


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

# }