Guide
radf() takes only two parameters, the window size and the lag length. The rest of a test's behaviour depends on the critical values you compare the statistic with. The GSADF statistic has no closed-form distribution, so every critical value is simulated, either once for a lookup table or from your own data.
Settings
exuber
minw default: (0.01 + 1.8/√T)·T
The minimum window size, in observations. If it is too short, the ADF regression inside the window has little power. If it is too long, early and short-lived bubbles fall below the floor and cannot be tested at all. The default is the rule of thumb of Phillips, Shi & Yu, which depends only on the sample size T. Pass an integer to override it.
lag default: 0
The number of lagged Δy terms in the ADF regression. This is the same augmentation as in an ordinary ADF test, applied inside every recursive window. It is fixed and defaults to 0. The precomputed critical values cover lags 0 to 4, so a run with lags needs no simulation of its own. For the sieve bootstrap, radf_sb_cv(type = "aic" / "bic") can choose the lag automatically, once per series.
Both are arguments to radf().
Its reference entry describes the return value and gives worked examples.
The other choice
The statistic from radf() needs a critical value before it
can be interpreted. There are three ways to get one. They are listed in order of
increasing computing cost, and each matches your data more closely than the last:
Monte Carlo tables simulated once for every T up to 4,000 and lags 0–4. They are fetched on first use and cached. You get these when you pass no cv.
Simulated under the null (a random walk) for your exact T and minw. This assumes homoskedastic Gaussian innovations. See radf_mc_cv().
Built from your own data, so it reproduces any heteroskedasticity or autocorrelation the data contain. The wild bootstrap (radf_wb_cv(), radf_wb_ps_cv()) and the sieve bootstrap (radf_sb_cv(), for panels) are both available.
Monte Carlo
Draw a pure random walk, cumsum(rnorm(n)), run GSADF on it,
and repeat. After a few thousand replications, the 90th, 95th and 99th percentiles of the
simulated distribution are the critical values for that sample size. They are exact for
that T and minw, but they assume homoskedastic Gaussian
innovations, which real series rarely have. See radf_mc_cv().
The default tables were built in this way, with 2,000 seeded replications for every lag
from 0 to 4 and every sample size up to 4,000. They are served as a lookup, so a typical
radf() call does not need to simulate anything (see the shared store below).
Wild bootstrap
Instead of drawing fresh Gaussian noise, fit the null model to the actual series, take its
residuals, and resample them with random ± sign weights in each replication. Any
heteroskedasticity in the data, such as volatility clustering, a variance break or fat
tails, carries over into the simulated critical value instead of being assumed away.
The method costs more, and its critical values apply to one dataset and cannot be reused
for other series. See radf_wb_cv().
Variants
radf_wb_cv(dist_skew = TRUE) draws Hafner's (2020) right-skewed multiplier weights. Use it for series whose returns are strongly right-skewed, such as the cryptocurrencies in the paper's own application.monitor() uses it for the training window. See radf_wb_ps_cv().radf_sb_cv().Multiple series
There is no separate panel setting. If you pass radf() a matrix or
data frame with more than one column, it computes the univariate statistics for every
series in one pass. It also returns bsadf_panel and
gsadf_panel, the cross-sectional average and its supremum,
at almost no extra cost. The panel statistic is tested against the panel critical values
from the sieve bootstrap (radf_sb_cv()).