urca (version 1.2-9)

ca.po: Phillips \& Ouliaris Cointegration Test

Description

Performs the Phillips \& 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().

Value

An object of class 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.

References

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

See Also

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)