ADF.test: Augmented Dickey-Fuller Test
In uroot: Unit Root Tests and Graphics for Seasonal Time Series

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2	ADF.test (wts, itsd, regvar=0, selectlags=list(mode="signf", Pmax=NULL))

`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 must be a vector object with the following elements: `c(0,0,c(0))`, if the first and/or second elements are set equal to 1, it indicates that an intercept, and/or linear trend, respectively, are included. The third element is a vector indicating which seasonal dummies should be included. If no seasonal dummies are desired it must be set equal to zero. For example, `regular=c(1,0,c(1,2,3))` would include an intercept, no trend, and the first three seasonal dummies.
`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` is a numeric object indicating the maximum lag order. By default, the maximum number of lags considered is round(10log10(n))*, where n is the number of observations.

The auxiliar regression is defined as,

δ y_t = ρ y_{t-1} + ε_t,

where δ is the first order operator. Hence, under the null hypothesis ρ=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.

An object of class adfstat-class.

Javier Lopez-de-Lacalle javlacalle@yahoo.es and Ignacio Diaz-Emparanza Ignacio.Diaz-Emparanza@ehu.es

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.

ADF.rectest.

    ## 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