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

## Description

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

## Usage

 ```1 2``` ``` 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 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(10*log10(n)), where n is the number of observations.

## Details

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.

## Value

An object of class `adfstat-class`.

## Author(s)

Javier Lopez-de-Lacalle [email protected] and Ignacio Diaz-Emparanza [email protected]

## 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.

`ADF.rectest`.
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` ## 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 ```