A New Test for Structural Stability Based on Recursive Residuals
| Author | Jonathan H. Wright |
| Published date | 01 February 1999 |
| Date | 01 February 1999 |
| DOI | http://doi.org/10.1111/1468-0084.00119 |
A NEW TEST FOR STRUCTURAL STABILITY BASED
ON RECURSIVE RESIDUALS
Jonathan H. Wrighty
I. INTRODUCTION
Tests for structural stability in which the researcher is not required to
specify the potential break date a priori have received considerable atten-
tion in the recent literature. These include the test proposed by Nyblom
(1989), the sup-F test and the CUSUM test based on OLS residuals. The
distribution theory for these tests depends on the data generating process of
the regressors. Most papers are concerned with working out asymptotic
theory under the assumption that the regressors are stationary (e.g. Nyblom
(1989), Andrews (1993), Ploberger and KraÈmer (1992)). Hansen (1992)
derived the null limiting distributions of these statistics in a cointegrating
regression when the regressors have unit roots (which differ from the
distributions in the stationary case). MacNeil (1978) derived the null limit-
ing distribution of the CUSUM test based on OLS residuals when the
regressors are polynomial trends. This again differs from the null limiting
distribution in the stationary case (and from the distribution in the unit root
case) and depends on the order of the polynomial trends. Also heteroskedas-
ticity in the regressors affects the asymptotic distribution of these stability
tests (Hansen (1994)).
The CUSUM and CUSUM of squares tests, based on recursive residuals,
have the signi®cant advantage over all the above listed tests that they have
distributions that do not depend on the data generating process of the
regressors. Notwithstanding this property, the tests are not widely used
because of their poor power properties. Ploberger and KraÈmer (1990)
showed that the CUSUM test has only trivial local asymptotic power against
the alternative of a break in the coef®cient on a stationary zero-mean
regressor and that the CUSUM of squares test has only trivial local
asymptotic power against the alternative of a break in any coef®cient. This
is discussed more precisely in section III. These tests have poor power
properties in Monte-Carlo simulations.
In this paper, I propose an exact test for a null of structural stability in a
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 61, 1 (1999)
0305-9049
109
#Blackwell Publishers Ltd, 1999. Published by Blackwell Publishers, 108 Cowley Road, Oxford
OX4 1JF,UK and 350 Main Street, Malden, MA 02148, USA.
yI am grateful to Guido Imbens, Jim Stock and Editors for helpful comments on earlier versions
of this manuscript. All errors are the sole responsibility of the author
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