Recursive Augmented Dickey-Fuller

Wild Bootstrap Critical Values

Also: radf_wb_distr

radf_wb_cv

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
)

radf_wb_cv generates critical values for the recursive unit root tests with the wild bootstrap of Harvey et al. (2016), which is asymptotically robust to non-stationary volatility. radf_wb_distr computes the distribution.

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).
dist_rad	Logical. If TRUE then the Rademacher distribution will be used.
dist_skew	Logical. If TRUE, use the fixed right-skewed multiplier distribution of Hafner (2020) instead of the default standard normal or (`dist_rad = TRUE`) Rademacher one. It is appropriate when the return distribution of the series is itself clearly right-skewed, as for the cryptocurrency returns in the application of that paper. 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. 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_cv, a list with the critical values for the ADF, BADF, BSADF and GSADF tests. For radf_wb_distr, a list with the ADF, SADF and GSADF distributions.

Details

The function applies a wild bootstrap re-sampling scheme to construct the bootstrap analogue of the test of Phillips et al. (2015). The bootstrap test is asymptotically robust to non-stationary volatility.

Examples

These examples are copied from the package's own documentation and are run by R CMD check on every release. The printed output (after #>) and the plots were produced by running them against the current package source.

# Volatility triples half-way through the sample. This is the case of
# non-stationary volatility that the wild bootstrap is built for, and 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)

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. 10.1111/iere.12132

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