R: Phillips-Perron Unit Root Test

pp.test {tseries} | R Documentation

## Phillips–Perron Unit Root Test

### Description

Computes the Phillips-Perron test for the null hypothesis that `x` has a unit root.

### 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.

### Author(s)

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.

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

### See Also

`adf.test`

### Examples

    x <- rnorm(1000)  # no unit-root
    pp.test(x)

    y <- cumsum(x)  # has unit root
    pp.test(y)

[Package tseries version 0.10-47 Index]