# adf.test: Augmented Dickey-Fuller Test In tseries: Time Series Analysis and Computational Finance

## Augmented Dickey–Fuller Test

### 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.

### 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.

A. Trapletti

### 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.

`pp.test`

### Examples

```x <- rnorm(1000)  # no unit-root