pCADFtest: Panel Covariate-Augmented Dickey Fuller (CADF) test for unit...

In punitroots: Unit Roots in Panels of Time Series

Description

This function implements the panel Covariate Augmented Dickey-Fuller (pCADF) test developed in Costantini and Lupi (2012). The panel unit root tests proposed in Choi (2001) and in Demetrescu et al. (2006) can also be performed using this function.

Usage

pCADFtest(Y, X=NULL, covariates=NULL, crosscorr=0.10, type="trend", 
     data=list(), max.lag.y=1, min.lag.X=0, max.lag.X=0, 
     dname=NULL, criterion=c("none", "BIC", "AIC", "HQC", 
     "MAIC"), ...)

Arguments

Y	a multiple time series or a T \times N matrix. It contains the series to be tested. The series may have different length.
X	a vector, a matrix, or a vector time series of stationary covariates. If no X is specified, then the tests proposed by Choi (2001) and Demetrescu et al. (2006) are performed. As an alternative, the pCADF test (Costantini and Lupi 2012) can also be performed with the stationary covariate(s) derived from Y.
covariates	a character or a vector of scalars containing integers from 1 to N. The default is NULL. When covariates = NULL then tests proposed in Choi (2001) or Demetrescu et al. (2006) are performed (no stationary covariates). If covariates = "PC", the stationary covariate is computed as the difference of the first principal component of Y and the same covariate is used for all the individual tests. If covariates = "DY", each individual test is carried out using the average of the other differenced Y. See Costantini and Lupi (2012) for details. Otherwise, covariates must be a vector of length equal to the number of columns of X. The first number will indicate which column of Y is associated to the first stationary covariate represented by the first column of X; the second number identifies the correspondence between a column of Y with the second column of X and so on.
crosscorr	a real scalar between 0 and 1. It is the threshold of the p-value of Pesaran's test for cross-correlation. If the actual test p-value is lower than crosscorr, then the correction proposed by Hartung (1999) is applied. if crosscorr = 0 the original p-value combination test developed by Choi (2001) for independent series is carried out. If crosscorr = 1 then Hartung's correction is always applied as in Demetrescu et al. (2006).
type	a character or a N-vector of characters. It defines the deterministic kernel to be used in the tests. It accepts the values used in package urca. It specifies if the underlying model must be with linear trend ("trend", the default), with constant ("drift") or without constant ("none"). When a character is passed to the procedure, then the same deterministic kernel is used for all the tests.
data	not used.
max.lag.y	maximum number of lags allowed for the lagged differences of the variable to be tested. Both a scalar integer or a N-vector of integers can be used. When using a scalar, the same maximum lag is used for all the series. Different maximum lags can be used for each series by defining a N-vector of integers.
min.lag.X	an integer scalar or an vector of integers. Same as max.lag.y. If negative it is the maximum lead allowed for the covariates. If zero, it is the minimum lag allowed for the covariates. When more than one covariate is used, the same min.lag.X is used for all the covariates.
max.lag.X	an integer scalar or an vector of integers. Maximum lag allowed for the covariates. Same as min.lag.X.
dname	NULL or character. It can be used to give a special name to the model. If the NULL default is accepted and the model is specified using a formula notation, then dname is computed according to the used formula.
criterion	it can be either "none" (the default), "BIC", "AIC", "HQC" or "MAIC". If criterion="none", no automatic model selection is performed. Otherwise, automatic model selection is performed using the specified criterion. In this case, the max and min orders serve as upper and lower bounds in the model selection.
...	Extra arguments that can be set to use special kernels, prewhitening, etc. in the estimation of ρ^2. A Quadratic kernel with a VAR(1) prewhitening is the default choice. To set these extra arguments to different values, see kernHAC in package sandwich (Zeileis, 2004, 2006). Other arguments can be passed also to the procedure that performs Hartung's correction.

Value

The function returns an object of class c("pCADFtest", "htest") containing:

statistic	the test statistic.
parameter	the estimated nuisance parameter ρ^2 (see Hansen, 1995, p. 1150).
method	the test performed: it can be either ADF or CADF.
p.value	the p-value of the test.
corr	logical. TRUE if Hartung correction has been applied, FALSE otherwise.
individual.tests	a N \times 5 matrix containing the values of the p.value, ρ^2, the orders p, q_1 and q_2 of each single test on each of the N time series.
Pesaran	the outcome of Pesaran's test for cross-dependence.

Author(s)

Claudio Lupi

References

Choi I (2001). Unit Root Tests for Panel Data, Journal of International Money and Finance, 20(2), 249–272.

Costantini M, Lupi C, (2012). A Simple Panel-CADF Test for Unit Roots. Oxford Bulletin of Economics \& Statistics, doi: 10.1111/j.1468-0084.2012.00690.x.

Hansen BE (1995). Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power, Econometric Theory, 11(5), 1148–1171.

Hartung J (1999). A Note on Combining Dependent Tests of Significance, Biometrical Journal, 41(7), 849–855.

Lupi C (2009). Unit Root CADF Testing with R, Journal of Statistical Software, 32(2), 1–19. http://www.jstatsoft.org/v32/i02/

Pesaran MH (2004). General Diagnostic Tests for Cross Section Dependence in Panels, University of Cambridge, mimeo.

Zeileis A (2004). Econometric Computing with HC and HAC Covariance Matrix Estimators, Journal of Statistical Software, 11(10), 1–17. http://www.jstatsoft.org/v11/i10/

Zeileis A (2006). Object-Oriented Computation of Sandwich Estimators, Journal of Statistical Software, 16(9), 1–16. http://www.jstatsoft.org/v16/i09/.

See Also

fUnitRoots, urca

Examples

data("OECDgdp")
Y <- log(OECDgdp)
Demetrescuetal.test <- pCADFtest(Y, max.lag.y = 2, criterion = "AIC")

punitroots documentation built on May 2, 2019, 5:16 p.m.