# pp.test

##### Phillips--Perron Unit Root Test

Computes the Phillips-Perron test for the null hypothesis that
`x`

has a unit root.

- Keywords
- ts

##### Usage

```
pp.test(x, alternative = c("stationary", "explosive"),
type = c("Z(alpha)", "Z(t_alpha)"), lshort = TRUE)
```

##### Arguments

- x
a numeric vector or univariate time series.

- alternative
indicates the alternative hypothesis and must be one of

`"stationary"`

(default) or`"explosive"`

. You can specify just the initial letter.- type
indicates which variant of the test is computed and must be one of

`"Z(alpha)"`

(default) or`"Z(t_alpha)"`

.- lshort
a logical indicating whether the short or long version of the truncation lag parameter is used.

##### Details

The general regression equation which incorporates a constant and a
linear trend is used and the `Z(alpha)`

or `Z(t_alpha)`

statistic for a first order autoregressive coefficient equals one are
computed. To estimate `sigma^2`

the Newey-West estimator is
used. If `lshort`

is `TRUE`

, then the truncation lag
parameter is set to `trunc(4*(n/100)^0.25)`

, otherwise
`trunc(12*(n/100)^0.25)`

is used. The p-values are interpolated
from Table 4.1 and 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 handled.

##### Value

A list with class `"htest"`

containing the following components:

the value of the test statistic.

the truncation lag parameter.

the p-value of the test.

a character string indicating what type of test was performed.

a character string giving the name of the data.

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.

P. Perron (1988):
Trends and Random Walks in Macroeconomic Time Series.
*Journal of Economic Dynamics and Control* **12**, 297--332.

##### See Also

##### Examples

```
# NOT RUN {
x <- rnorm(1000) # no unit-root
pp.test(x)
y <- cumsum(x) # has unit root
pp.test(y)
# }
```

*Documentation reproduced from package tseries, version 0.10-47, License: GPL-2*