# 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: statistic the value of the test statistic. parameter the truncation lag parameter. 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.
P. Perron (1988):
Trends and Random Walks in Macroeconomic Time Series.
*Journal of Economic Dynamics and Control* **12**, 297--332.

##### See Also

##### Examples

```
x <- rnorm(1000) # no unit-root
pp.test(x)
y <- cumsum(x) # has unit root
pp.test(y)
```

*Documentation reproduced from package tseries, version 0.9-21, License: GPL (see file COPYING)*