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 0.10-0

Index]