uroot (version 1.4-1)

ADF.test: Augmented Dickey-Fuller Test

Description

This function computes the augmented Dickey-Fuller statistic for testing the null hypothesis that the long run unit root 1 exists.

Usage

ADF.test (wts, itsd, regvar=0, selectlags=list(mode="signf", Pmax=NULL))

Arguments

wts

a univariate time series object.

itsd

deterministic components to include in the model. Three types of regressors can be included: regular deterministic components, seasonal deterministic components, and any regressor variable previously defined by the user.

This argument m

regvar

regressor variables. If none regressor variables are considered, this object must be set equal to zero, otherwise, the names of a matrix object previously defined should be indicated.

selectlags

lag selection method. A list object indicating the method to select lags, mode, and the maximum lag considered. Available methods are "aic", "bic", and "signf". See details. Pmax

Value

• An object of class adfstat-class.

Details

The auxiliar regression is defined as,

$\delta y_t = \rho y_{t-1} + \epsilon_t,$

where $\delta$ is the first order operator. Hence, under the null hypothesis $\rho=0$ and the long run unit root 1 exists.

Available methods are the following. "aic" and "bic" follows a top-down strategy based on the Akaike's and Schwarz's information criteria, and "signf" removes the non-significant lags at the 10% level of significance until all the selected lags are significant. By default, the maximum number of lags considered is $round(10*log10(n))$, where $n$ is the number of observations.

It is also possible to set the argument selectlags equals to a vector, mode=c(1,3,4), then those lags are directly included in the auxiliar regression and Pmax is ignored.

References

D.A. Dickey and W.A. Fuller (1981), Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49, 1057-1071.

W.A. Fuller (1976), Introduction to Statistical Time Series. Jonh Wiley, New York.

See Also

ADF.rectest.

Examples

## ADF test with constant, trend and seasonal dummies.
    data(AirPassengers)
    lairp <- log(AirPassengers)
    adf.out1 <- ADF.test(wts=lairp, itsd=c(1,1,c(1:11)),
                  regvar=0, selectlags=list(mode="bic", Pmax=12))
    adf.out1
    adf.out2 <- ADF.test(wts=lairp, itsd=c(1,1,c(1:11)),
                  regvar=0, selectlags=list(mode="signf", Pmax=NULL))
    adf.out2