Phillips–Ouliaris Cointegration Test
po.test.RdComputes the Phillips-Ouliaris test for the null hypothesis that
x is not cointegrated.
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, page 189 of
Phillips+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.
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
#>