tseries (version 0.8-0)

pp.test: 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.

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.

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.

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)