Phillips–Ouliaris Cointegration Test
Computes the Phillips-Ouliaris test for the null hypothesis that
x is not cointegrated.
po.test(x, demean = TRUE, lshort = TRUE)
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. |
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.
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. |
A. Trapletti
P. C. B. Phillips and S. Ouliaris (1990): Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica 58, 165–193.
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)
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