# adf.test {tseries}

### Description

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

has a unit root.

### 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.

### Values

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

`pp.test`

### Examples

Documentation reproduced from package tseries, version 0.10-32. License: GPL-2