# po.test

0th

Percentile

##### Phillips--Ouliaris Cointegration Test

Computes the Phillips-Ouliaris test for the null hypothesis that x is not cointegrated.

Keywords
ts
##### Usage
po.test(x, demean = TRUE, lshort = TRUE)
##### Arguments
x
a matrix or multivariate time series.
demean
a logical indicating whether an intercept is included in the cointegration regression or not.
lshort
a logical indicating whether the short or long version of the truncation lag parameter is used.
##### Details

The Phillips-Perron Z(alpha) statistic for a unit root in the residuals of the cointegration regression is computed, see also pp.test. The unit root is estimated from a regression of the first variable (column) of x on the remaining variables of x without a constant and a linear trend. To estimate sigma^2 the Newey-West estimator is used. If lshort is TRUE, then the truncation lag parameter is set to trunc(n/100), otherwise trunc(n/30) is used. The p-values are interpolated from Table Ia and Ib, p. 189 of Phillips and Ouliaris (1990). If the computed statistic is outside the table of critical values, then a warning message is generated. The dimension of x is restricted to six variables. Missing values are not handled.

##### Value

• A list with class "htest" containing the following components:
• statisticthe value of the test statistic.
• parameterthe truncation lag parameter.
• p.valuethe p-value of the test.
• methoda character string indicating what type of test was performed.
• data.namea character string giving the name of the data.

##### References

P. C. B. Phillips and S. Ouliaris (1990): Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica 58, 165--193.

pp.test

• po.test
##### Examples
x <- ts(diffinv(matrix(rnorm(2000),1000,2)))  # no cointegration
po.test(x)

x <- diffinv(rnorm(1000))
y <- 2.0-3.0*x+rnorm(x,sd=5)
z <- ts(cbind(x,y))  # cointegrated
po.test(z)
Documentation reproduced from package tseries, version 0.9-20, License: GPL (see file COPYING)

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