CADFtest {CADFtest}R Documentation

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

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. Automatic model selection is allowed.

Usage

CADFtest(model, X=NULL, trend=c("c", "nc", "ct", "none", "drift", "trend"), 
                             data=list(), max.lag.y=1, min.lag.X=0, max.lag.X=0, dname="",
                             Auto=FALSE, criterion=c("BIC", "AIC"), prewhite=FALSE,
                             kernel = c("Parzen", "Quadratic Spectral", "Truncated", "Bartlett", "Tukey-Hanning"))

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 model=y is specified where y is a vector or a time series, then an ordinary ADF test is performed. It is not the actual model, it 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.
trend defines the deterministic kernel used in the test. It accepts the values used either in fUnitRoots or urca packages. It specifies if the underlying model must be with constant ("c" or "drift", the default), without constant ("nc" or "none"), or with constant and trend ("ct" or "trend").
data data to be used (optional).
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 character. Data name. In general there is no need to modify the default value. The correct data name is computed on the basis of the model passed to the function.
Auto logical. If Auto==FALSE then the test is performed using the given orders of lags and leads. If Auto==TRUE then the test is performed using the model that minimizes the selection citerion defined in criterion. In this case, the max e min orders serve as upper and lower bounds in the model selection.
criterion it can be either "BIC" or "AIC". It is effective only when Auto==T.
prewhite logical or integer. Should the estimating functions be prewhitened? If TRUE or greater than 0 a VAR model of order as.integer(prewhite) is fitted via ar with method "ols" and demean = FALSE. The default is to use no prewhitening (prewhite = FALSE).
kernel a character specifying the kernel used. All kernels used are described in Andrews (1991).

Value

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

statistic the t test statistic.
parameter the nuisance rho2 parameter.
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.
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.

Note

If p-values are used, please cite Costantini, Lupi and Popp (2007).

Author(s)

Claudio Lupi

References

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

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

See Also

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, trend="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
  CADFt <- CADFtest(L.gnpperca~D.unemrate, data=S, trend="ct", max.lag.y=3)

[Package CADFtest version 0.1-0 Index]