Small Sample Testing For Unit Roots†
| Published date | 01 November 1992 |
| DOI | http://doi.org/10.1111/j.1468-0084.1992.mp54004010.x |
| Author | R. I. D. Harris |
| Date | 01 November 1992 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 54,4(1992)
0305-9049 $3.00
Small Sample Testing For Unit Rootst
R. I. D. Harris
I. INTRODUCTION
In a recent paper in this BULLETIN, Blangiewicz and Charemza (1990)
consider the problem of small-sample applications of existing unit root tests.
They point out that such small sample applications are beset by a lack of
knowledge of the percentiles of distributions, and thus the power, of the unit
root tests. Furthermore they note that '...the discrepancies between data
(and consequently between the small-sample distributions) generated by
different models are likely to be substantial.. .(Moreover) it is practically
impossible to construct tables of critical values which cover every possible
case' (Blangiewicz and Charemza, op. cit., p. 310). Their solution is to
generate 'customized' percentiles individually for different applications. To
do this they postulate a theoretical data generating process in order to simu-
late distributions under the null hypothesis of a unit root, from which critical
values can be obtained for the test statistics calculated for the actual empirical
model under examination. This short note offers an alternative approach,
based on the actual data generating process (d.p.g.) alone, that can be applied
to tests of integration for eachy,, as well as tests for cointegration.
In Section II there is a brief overview of commonly used unit root tests,
together with a discussion of the use of the augmented Dickey-Fuller test to
simulate distributions under the null and alternative hypothesis. Section III
provides an example applied to Chinese data.
II. UNIT ROOT TESTS
A number of tests for a unit root have been proposed, with the most popular
being the Sárgan-Bhargava (1983) CRDW test, the Dickey-Fuller (DF) test,
the augmented Dickey-Fuller (ADF) test, and the tests developed by Phillips
and Perron based on the Phillips (1987) Z test.1 The model favoured by
Dickey and Fuller (1981), and considered here, can be written as.
Ii am grateful to the Editors of this Journal and Professor Basawa for helpful comments.
Initial work benefited from discussion with Wally Thurman. Any errors remain solely my
responsibility.
'See Phillips and Perron (1988); Perron (1988); and Phillips and Ouliaris (1990).
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