Za: Phillips' (1987) Za and Zt Test for Unit Root

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

Phillips' (1987) Za and Zt Test for Unit Root

Description

Compute Phillips' (1987) Za and Zt statistics for the null hypothesis that y has a unit root.

Usage

Za(y,p=1,v=15,ker_fun="parzen",aband=0,filter=0)

Arguments

y	The data of dependent variable in a regression.
p	Order of the time polynomial in the cointegrating regressio. 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. Critical values are available for p within [1,5].
v	Number of autocovariance terms to compute the spectrum at frequency zero, default=15.
ker_fun	Set kernel function to one of the available kernels, default="parzen". See section details below.
aband	Whether to activate the automatic bandwidth selection. aband=1. To activate. aband=0. Do not activate.The default.
filter	Whether to use an AR(1) filter to compute the spectrum at frequency zero. filter=1. To use. filter=0. Do not use. The default.

Value

alpha	Estimate of the AR(1) coefficient.
za	Za statistic for the series under the null has a unit root. Reject the null hypothesis of a unit root if the test statistic < critical value.
za_cv	Critical values of Za.
zt	Zt statistic for the series under the null has a unit root. Reject the null hypothesis of a unit root if the test statistic < critical value.
zt_cv	Critical values of Zt.

Author(s)

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

References

Ouliaris, S., J. Y. Park, and P. C. B. Phillips (1989) Testing for a Unit Root in the Presence of a Maintained Trend. Ch. 1 in Baldev Raj (ed.), Advances in Econometrics and Modelling. Netherlands: Kluwer Academic Publishers.
Phillips, P. C. B. (1987) Time Series Regression with a Unit Root. Econometrica, 55, 277-301.

Examples

data(macro)
y=macro[,1]
Za(y,p=1,v=10)

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