# po.test

##### Phillips--Ouliaris Cointegration Test

Computes the Phillips-Ouliaris test for the null hypothesis that
`x`

is not cointegrated.

- Keywords
- ts

##### 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.

##### References

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

##### See Also

##### 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)
```

*Documentation reproduced from package tseries, version 0.9-19, License: GPL (see file COPYING)*