Hansen's Covariate-Augmented Dickey Fuller (CADF) test for unit roots

Description

This function is an interface to CADFtest.default that computes the CADF unit root test proposed in Hansen (1995). The asymptotic p-values of the test are also computed along the lines proposed in Costantini et al. (2007). Automatic model selection is allowed. A full description and some applications can be found in Lupi (2009).

Usage

CADFtest(model, X=NULL, type=c("trend", "drift", "none"),
data=list(), max.lag.y=1, min.lag.X=0, max.lag.X=0,
dname=NULL, criterion=c("none", "BIC", "AIC", "HQC",
"MAIC"), ...)


Arguments

 model a formula of the kind y ~ x1 + x2 containing the variable y to be tested and the stationary covariate(s) to be used in the test. If the model is specified as y ~ 1, then an ordinary ADF is carried out. Note that the specification y ~ . here does not imply a model with all the disposable regressors, but rather a model with no stationary covariate (which correspons to an ADF test). This is because the stationary covariates have to be explicitly indicated (they are usually one or two). An ordinary ADF is performed also if model=y is specified, where y is a vector or a time series. It should be noted that model is not the actual model, but rather a representation that is used to simplify variable specification. The covariates are assumed to be stationary. X if model=y, a matrix or a vector time series of stationary covariates X can be passed directly, instead of using the formula expression. However, the formula expression should in general be preferred. type defines the deterministic kernel used in the test. 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"). data data to be used (optional). This argument is effective only when model is passed as a formula. max.lag.y maximum number of lags allowed for the lagged differences of the variable to be tested. min.lag.X if negative it is maximum lead allowed for the covariates. If zero, it is the minimum lag allowed for the covariates. max.lag.X maximum lag allowed for the covariates. 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 \rho^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). If Hansen's results have to be duplicated, then kernel="Parzen" and prewhite=FALSE must be specified.

Value

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

 statistic the t test statistic. parameter the estimated nuisance parameter \rho^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. data.name the data name. max.lag.y the maximum lag of the differences of the dependent variable. min.lag.X the maximum lead of the stationary covariate(s). max.lag.X the maximum lag of the stationary covariate(s). AIC the value of the AIC for the selected model. BIC the value of the BIC for the selected model. HQC the value of the HQC for the selected model. MAIC the value of the MAIC for the selected model. est.model the estimated model. estimate the estimated value of the parameter of the lagged dependent variable. null.value the value of the parameter of the lagged dependent variable under the null. alternative the alternative hypothesis. call the call to the function. type the deterministic kernel used.

Claudio Lupi

References

Costantini M, Lupi C, Popp S (2007). A Panel-CADF Test for Unit Roots, University of Molise, Economics & Statistics Discussion Paper 39/07. http://econpapers.repec.org/paper/molecsdps/esdp07039.htm

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

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

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/.

fUnitRoots, urca

Examples

##---- ADF test on extended Nelson-Plosser data ----
##--   Data taken from package urca
data(npext, package="urca")
ADFt <- CADFtest(npext$gnpperca, max.lag.y=3, type="trend") ##---- CADF test on extended Nelson-Plosser data ---- data(npext, package="urca") npext$unemrate <- exp(npext\$unemploy)      # compute unemployment rate
L <- ts(npext, start=1860)                 # time series of levels
D <- diff(L)                               # time series of diffs
S <- window(ts.intersect(L,D), start=1909) # select same sample as Hansen's