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.

A. Trapletti

### References

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

`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]