# adf.test

##### Augmented Dickey--Fuller Test

Computes the Augmented Dickey-Fuller test for the null that `x`

has
a unit root.

- Keywords
- ts

##### Usage

```
adf.test(x, alternative = c("stationary", "explosive"),
k = trunc((length(x)-1)^(1/3)))
```

##### Arguments

- x
- a numeric vector or time series.
- alternative
- indicates the alternative hypothesis and must be
one of
`"stationary"`

(default) or`"explosive"`

. You can specify just the initial letter. - k
- the lag order to calculate the test statistic.

##### Details

The general regression equation which incorporates a constant and a
linear trend is used and the t-statistic for a first order
autoregressive coefficient equals one is computed. The number of lags
used in the regression is `k`

. The default value of
`trunc((length(x)-1)^(1/3))`

corresponds to the suggested upper
bound on the rate at which the number of lags, `k`

, should be
made to grow with the sample size for the general `ARMA(p,q)`

setup. Note that for `k`

equals zero the standard Dickey-Fuller
test is computed. The p-values are interpolated from Table 4.2, p. 103
of Banerjee et al. (1993). If the computed statistic is outside the
table of critical values, then a warning message is generated.
Missing values are not allowed.

##### Value

- A list with class
`"htest"`

containing the following components: statistic the value of the test statistic. parameter the lag order. p.value the p-value of the test. method a character string indicating what type of test was performed. data.name a character string giving the name of the data. alternative a character string describing the alternative hypothesis.

##### References

A. Banerjee, J. J. Dolado, J. W. Galbraith, and D. F. Hendry (1993):
*Cointegration, Error Correction, and the Econometric Analysis of
Non-Stationary Data*,
Oxford University Press, Oxford.
S. E. Said and D. A. Dickey (1984):
Testing for Unit Roots in Autoregressive-Moving Average Models of
Unknown Order.
*Biometrika* **71**, 599--607.

##### See Also

##### Examples

```
x <- rnorm(1000) # no unit-root
adf.test(x)
y <- diffinv(x) # contains a unit-root
adf.test(y)
```

*Documentation reproduced from package tseries, version 0.8-3, License: GPL (see file COPYING), except for ./src/muin2ser.f and ./misc which are free for non-commercial purposes. See file README for details.*