# ca.po: Phillips and Ouliaris Cointegration Test In urca: Unit Root and Cointegration Tests for Time Series Data

 ca.po R Documentation

## Phillips and Ouliaris Cointegration Test

### Description

Performs the Phillips and Ouliaris `"Pu"` and `"Pz"` cointegration test.

### Usage

```ca.po(z, demean = c("none", "constant", "trend"),
lag = c("short", "long"), type = c("Pu", "Pz"), tol = NULL)
```

### Arguments

 `z` Data matrix to be investigated for cointegration. `demean` The method for detrending the series, either `"none"`, `"constant"` or `"trend"`. `lag` Either a short or long lag number used for variance/covariance correction. `type` The test type, either `"Pu"` or `"Pz"`. `tol` Numeric, this argument is passed to `solve()` in `ca.po()`.

### Details

The test `"Pz"`, compared to the test `"Pu"`, has the advantage that it is invariant to the normalization of the cointegration vector, i.e. it does not matter which variable is on the left hand side of the equation. In case convergence problems are encountered by matrix inversion, one can pass a higher tolerance level via `"tol=..."` to the `solve()`-function.

### Value

An object of class `ca.po`.

Bernhard Pfaff

### References

Phillips, P.C.B. and Ouliaris, S. (1990), Asymptotic Properties of Residual Based Tests for Cointegration, Econometrica, Vol. 58, No. 1, 165–193.

`ca.po-class`

### Examples

```data(ecb)
m3.real <- ecb[,"m3"]/ecb[,"gdp.defl"]
gdp.real <- ecb[,"gdp.nom"]/ecb[,"gdp.defl"]
rl <- ecb[,"rl"]
ecb.data <- cbind(m3.real, gdp.real, rl)
m3d.po <- ca.po(ecb.data, type="Pz")
summary(m3d.po)
```

urca documentation built on Aug. 30, 2022, 1:10 a.m.