CZa: Phillips' (1987) Za and Zt test for cointegration

In COINT: Unit Root Tests with Structural Breaks and Fully-Modified Estimators

Phillips' (1987) Za and Zt test for cointegration

Description

Test the null hypothesis of no cointegration between y and x using Phillips' (1987) Za and Zt statistics and Phillips and Ouliaris (1990) limit theory.

Usage

CZa(y,x,p=1,v=15)

Arguments

y	The data of dependent variable in a regression.
x	The data of independent variables in a regression.
p	Order of the time polynomial in the cointegrating regressio. Critical values are available for p within [1,5]. p =-1: No deterministic term in the cointegrating regression. p = 0: For a constant term. p = 1: For a constant term and trend. Default. P > 2: For time polynomial.
v	Number of autocovariance terms to compute the spectrum at frequency zero, default=15.

Value

alpha	Estimate of the AR(1) coefficient.
cza	Za statistic for non-cointegration.Reject the null hypothesis of no cointegration if the Z statistic < critical value.
cza_cv	Critical values of cza.
czt	Zt statistic for non-cointegration.Reject the null hypothesis of no cointegration if the Z statistic < critical value.
czt_cv	Critical values of czt.

Author(s)

Ho Tsung-wu <[e-mail]>, College of Management, National Taiwan Normal University.

References

Phillips, P. C. B. (1987) Time Series Regression with a Unit Root. Econometrica, 55, 277-301.
Phillips, P. C. B. and Ouliaris S. (1990) Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica, 58, 165-193.

Examples

data(macro)
y=macro[,1]
x=macro[,-1]
CZa(y,x,p=1,v=10)

COINT documentation built on Sept. 9, 2025, 5:51 p.m.