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)

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:

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.

References

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

Author

A. Trapletti

Examples

x <- ts(diffinv(matrix(rnorm(2000),1000,2)))  # no cointegration
po.test(x)
#> Warning: p-value greater than printed p-value
#> 
#> 	Phillips-Ouliaris Cointegration Test
#> 
#> data:  x
#> Phillips-Ouliaris demeaned = -4.3291, Truncation lag parameter = 10,
#> p-value = 0.15
#> 

x <- diffinv(rnorm(1000))
y <- 2.0-3.0*x+rnorm(x,sd=5)
z <- ts(cbind(x,y))  # cointegrated
po.test(z)
#> Warning: p-value smaller than printed p-value
#> 
#> 	Phillips-Ouliaris Cointegration Test
#> 
#> data:  z
#> Phillips-Ouliaris demeaned = -1071.1, Truncation lag parameter = 10,
#> p-value = 0.01
#>