boot_adf {bootUR}R Documentation

Bootstrap augmented Dickey-Fuller Unit Root Test

Description

This function performs a standard augmented Dickey-Fuller 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 T-dimensional vector to be tested for unit roots. Data may also be in a time series format (e.g. ts, zoo or xts), or a data frame.

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

"MBB"

Moving blocks bootstrap (Paparoditis and Politis, 2003);

"BWB"

Block wild bootstrap (Shao, 2011);

"DWB"

Dependent wild bootstrap (Shao, 2010; Rho and Shao, 2019);

"AWB"

Autoregressive wild bootstrap (Smeekes and Urbain, 2014a; Friedrich, Smeekes and Urbain, 2020), this is the default;

"SB"

Sieve bootstrap (Chang and Park, 2003; Palm, Smeekes and Urbain, 2008; Smeekes, 2013);

"SWB"

Sieve wild bootstrap (Cavaliere and Taylor, 2009; Smeekes and Taylor, 2012).

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 0.01^(1/block_length) as in Smeekes and Urbain (2014a); this can be overwritten by setting ar_AWB directly. Default sets the block length as a function of the time series length T, via the rule block_length = 1.75 T^(1/3) of Palm, Smeekes and Urbain (2011).

ar_AWB

Autoregressive parameter used in the AWB bootstrap method (bootstrap = "AWB"). Can be used to set the parameter directly rather than via the default link to the block length.

deterministics

String indicating the deterministic specification. Only relevant if union = FALSE. Options are

"none": no deterministics;

"intercept": intercept only;

"trend": intercept and trend.

If union = FALSE, the default is adding an intercept (a warning is given).

min_lag

Minimum lag length in the augmented Dickey-Fuller regression. Default is 0.

max_lag

Maximum lag length in the augmented Dickey-Fuller regression. Default uses the sample size-based rule 12(T/100)^{1/4}.

criterion

String for information criterion used to select the lag length in the augmented Dickey-Fuller regression. Options are: "AIC", "BIC", "MAIC", "MBIC". Default is "MAIC" (Ng and Perron, 2001).

detrend

String indicating the type of detrending to be performed. Only relevant if union = FALSE. Options are: "OLS" or "QD" (typically also called GLS, see Elliott, Rothenberg and Stock, 1996). The default is "OLS".

criterion_scale

Logical indicator whether or not to use the rescaled information criteria of Cavaliere et al. (2015) (TRUE) or not (FALSE). Default is TRUE.

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 Dickey-Fuller test, while detrend = "QD" provides the DF-GLS 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 difference-based 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 data-driven lag length selection with a pre-specified 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 p-value of the unit root test;

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, as boot_ur is specifically suited for that.

References

Chang, Y. and Park, J. (2003). A sieve bootstrap for the test of a unit root. Journal of Time Series Analysis, 24(4), 379-400.

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), 512-536.

Elliott, G., Rothenberg, T.J., and Stock, J.H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813-836.

Friedrich, M., Smeekes, S. and Urbain, J.-P. (2020). Autoregressive wild bootstrap inference for nonparametric trends. Journal of Econometrics, 214(1), 81-109.

Ng, S. and Perron, P. (2001). Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power. Econometrica, 69(6), 1519-1554,

Palm, F.C., Smeekes, S. and Urbain, J.-P. (2008). Bootstrap unit root tests: Comparison and extensions. Journal of Time Series Analysis, 29(1), 371-401.

Paparoditis, E. and Politis, D.N. (2003). Residual-based block bootstrap for unit root testing. Econometrica, 71(3), 813-855.

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), 12-19.

Rho, Y. and Shao, X. (2019). Bootstrap-assisted unit root testing with piecewise locally stationary errors. Econometric Theory, 35(1), 142-166.

Smeekes, S. (2013). Detrending bootstrap unit root tests. Econometric Reviews, 32(8), 869-891.

Shao, X. (2010). The dependent wild bootstrap. Journal of the American Statistical Association, 105(489), 218-235.

Shao, X. (2011). A bootstrap-assisted spectral test of white noise under unknown dependence. Journal of Econometrics, 162, 213-224.

Smeekes, S. and Taylor, A.M.R. (2012). Bootstrap union tests for unit roots in the presence of nonstationary volatility. Econometric Theory, 28(2), 422-456.

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

boot_ur

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)

[Package bootUR version 0.4.2 Index]