R: Phillips-Ouliaris Cointegration Test

po.test {tseries} | R Documentation

## Phillips–Ouliaris Cointegration Test

### Description

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

### 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:

`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.

### Author(s)

A. Trapletti

### References

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

### See Also

`pp.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)

[Package tseries version 0.10-47 Index]