pp.test: Phillips-Perron Unit Root Test

In tseries: Time Series Analysis and Computational Finance

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 \bibcitetR:Banerjee+Dolado+Galbraith: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

\bibshow

R:Banerjee+Dolado+Galbraith:1993, Perron:1988

See Also

adf.test

Examples

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

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

tseries documentation built on Feb. 18, 2026, 9:07 a.m.