"Unit Root Testing with Unstable Volatility"


Brendan K. Beare
	Nuffield College, Oxford University

	


Abstract

It is known that unit root test statistics may not have the usual asymptotic properties
when the variance of innovations is unstable. In particular, persistent changes in volatility can
cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of
modified unit root test statistics that are robust to the presence of unstable volatility. The modification
is achieved by purging heteroskedasticity from the data using a kernel estimate of volatility
prior to the application of standard tests. In the absence of deterministic trend components, this
approach delivers test statistics that achieve standard asymptotics under the null hypothesis of a
unit root. When the data are homoskedastic, the local power of unit root tests is unchanged by
our modification. We use Monte Carlo simulations to compare the finite sample performance of our
modified tests with that of existing methods of correcting for unstable volatility.


Keywords: unit root, heteroskedasticity, nonstationary volatility.

JEL Classification: C14, C22.