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)
- a matrix or multivariate time series.
- a logical indicating whether an intercept is included in the cointegration regression or not.
- 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
TRUE, then the truncation lag parameter is set to
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.
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)