boot_adf {bootUR}  R Documentation 
Bootstrap augmented DickeyFuller Unit Root Test
Description
This function performs a standard augmented DickeyFuller bootstrap unit root test on a single time series.
Usage
boot_adf(data, data_name = NULL, bootstrap = "AWB", B = 1999,
block_length = NULL, ar_AWB = NULL, deterministics = "intercept",
min_lag = 0, max_lag = NULL, criterion = "MAIC", detrend = "OLS",
criterion_scale = TRUE, show_progress = TRUE, do_parallel = TRUE,
cores = NULL)
Arguments
data 
A 
data_name 
Optional name for the data, to be used in the output. The default uses the name of the 'data' argument. 
bootstrap 
String for bootstrap method to be used. Options are

B 
Number of bootstrap replications. Default is 1999. 
block_length 
Desired 'block length' in the bootstrap. For the MBB, BWB and DWB bootstrap, this is a genuine block length. For the AWB bootstrap, the block length is transformed into an autoregressive parameter via the formula 
ar_AWB 
Autoregressive parameter used in the AWB bootstrap method ( 
deterministics 
String indicating the deterministic specification. Only relevant if
If 
min_lag 
Minimum lag length in the augmented DickeyFuller regression. Default is 0. 
max_lag 
Maximum lag length in the augmented DickeyFuller regression. Default uses the sample sizebased rule 
criterion 
String for information criterion used to select the lag length in the augmented DickeyFuller regression. Options are: 
detrend 
String indicating the type of detrending to be performed. Only relevant if 
criterion_scale 
Logical indicator whether or not to use the rescaled information criteria of Cavaliere et al. (2015) ( 
show_progress 
Logical indicator whether a bootstrap progress update should be printed to the console. Default is FALSE. 
do_parallel 
Logical indicator whether bootstrap loop should be executed in parallel. Default is TRUE. 
cores 
The number of cores to be used in the parallel loops. Default is to use all but one. 
Details
The options encompass many test proposed in the literature. detrend = "OLS"
gives the standard augmented DickeyFuller test, while detrend = "QD"
provides the DFGLS test of Elliott, Rothenberg and Stock (1996). The bootstrap algorithm is always based on a residual bootstrap (under the alternative) to obtain residuals rather than a differencebased bootstrap (under the null), see e.g. Palm, Smeekes and Urbain (2008).
Lag length selection is done automatically in the ADF regression with the specified information criterion. If one of the modified criteria of Ng and Perron (2001) is used, the correction of Perron and Qu (2008) is applied. For very short time series (fewer than 50 time points) the maximum lag length is adjusted downward to avoid potential multicollinearity issues in the bootstrap. To overwrite datadriven lag length selection with a prespecified lag length, simply set both the minimum 'min_lag' and maximum lag length 'max_lag' for the selection algorithm equal to the desired lag length.
Value
An object of class "bootUR"
, "htest"
with the following components:
method 
The name of the hypothesis test method; 
data.name 
The name of the data on which the method is performed; 
null.value 
The value of the (gamma) parameter of the lagged dependent variable in the ADF regression under the null hypothesis. Under the null, the series has a unit root. Testing the null of a unit root then boils down to testing the significance of the gamma parameter; 
alternative 
A character string specifying the direction of the alternative hypothesis relative to the null value. The alternative postulates that the series is stationary; 
estimate 
The estimated value of the (gamma) parameter of the lagged dependent variable in the ADF regression.; 
statistic 
The value of the test statistic of the unit root test; 
p.value 
The pvalue of the unit root test; 
details 
A list containing the detailed outcomes of the performed test, such as selected lags, individual estimates and pvalues. 
specifications 
The specifications used in the test. 
Errors and warnings
Error: Multiple time series not allowed. Switch to a multivariate method such as boot_ur, or change argument data to a univariate time series.
The function is a simple wrapper around
boot_ur
to facilitate use for single time series. It does not support multiple time series, asboot_ur
is specifically suited for that.
References
Smeekes, S. and Wilms, I. (2023). bootUR: An R Package for Bootstrap Unit Root Tests. Journal of Statistical Software, 106(12), 139.
Chang, Y. and Park, J. (2003). A sieve bootstrap for the test of a unit root. Journal of Time Series Analysis, 24(4), 379400.
Cavaliere, G. and Taylor, A.M.R (2009). Heteroskedastic time series with a unit root. Econometric Theory, 25, 1228–1276.
Cavaliere, G., Phillips, P.C.B., Smeekes, S., and Taylor, A.M.R. (2015). Lag length selection for unit root tests in the presence of nonstationary volatility. Econometric Reviews, 34(4), 512536.
Elliott, G., Rothenberg, T.J., and Stock, J.H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813836.
Friedrich, M., Smeekes, S. and Urbain, J.P. (2020). Autoregressive wild bootstrap inference for nonparametric trends. Journal of Econometrics, 214(1), 81109.
Ng, S. and Perron, P. (2001). Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power. Econometrica, 69(6), 15191554,
Palm, F.C., Smeekes, S. and Urbain, J.P. (2008). Bootstrap unit root tests: Comparison and extensions. Journal of Time Series Analysis, 29(1), 371401.
Paparoditis, E. and Politis, D.N. (2003). Residualbased block bootstrap for unit root testing. Econometrica, 71(3), 813855.
Perron, P. and Qu, Z. (2008). A simple modification to improve the finite sample properties of Ng and Perron's unit root tests. Economic Letters, 94(1), 1219.
Rho, Y. and Shao, X. (2019). Bootstrapassisted unit root testing with piecewise locally stationary errors. Econometric Theory, 35(1), 142166.
Smeekes, S. (2013). Detrending bootstrap unit root tests. Econometric Reviews, 32(8), 869891.
Shao, X. (2010). The dependent wild bootstrap. Journal of the American Statistical Association, 105(489), 218235.
Shao, X. (2011). A bootstrapassisted spectral test of white noise under unknown dependence. Journal of Econometrics, 162, 213224.
Smeekes, S. and Taylor, A.M.R. (2012). Bootstrap union tests for unit roots in the presence of nonstationary volatility. Econometric Theory, 28(2), 422456.
Smeekes, S. and Urbain, J.P. (2014a). A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing. GSBE Research Memorandum No. RM/14/008, Maastricht University
See Also
Examples
# boot_adf on GDP_BE
GDP_BE_adf < boot_adf(MacroTS[, 1], B = 199, deterministics = "trend", detrend = "OLS",
do_parallel = FALSE, show_progress = FALSE)
print(GDP_BE_adf)