A NOTE ON SZROETER'S BOUNDS TEST
| Date | 01 August 1981 |
| Author | Maxwell L. King |
| DOI | http://doi.org/10.1111/j.1468-0084.1981.mp43003006.x |
| Published date | 01 August 1981 |
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A NOTE ON SZROETER'S BOUNDS TEST
Maxwell L. King
I. INTRODUCTION
Recently, Harrison (1980) expressed surprise at the apparent reluctance
of researchers to test for heteroscedasticity in economic applications
of the linear regression model, in contrast with their obvious concern
for the possible presence of serially correlated disturbances. He con-
jectured that this curious trend might be because most tests for hetero-
scedasticity require considerably more computation than the simple
Durbin-Watson (DW) bounds procedure. While most computer re-
gression packages calculate the DW test statistic automatically, very
few calculate statistics appropriate for testing for heteroscedasticity.
Of the various tests that seem suitable for inclusion in regression
programs, Harrison considers Szroeter's (1978) bounds test, which
uses the DW tables for bounds on its critical values, to be particularly
attractive, both from the point of view of power and ease of applica-
tion. An examination of its small sample properties revealed it to be
subject to a high incidence of inconclusiveness. Harrison proposed
two supplementary procedures for circumventing this problem.
The purpose of this note is to show how Szroeter's procedure can be
made more analogous to the DW procedure thus making it more attrac-
tive for routine use. In particular, tables of bounds are presented that
reduce the degree of inconclusiveness for regressions with an intercept
term to a level which is comparable to that of the DW procedure.
II. DISCUSSION
Consider the usual linear regression model
y - Xß + u, (1)
where y is n X 1, X is an n X k nonstochastic matrix of observations
on k explanatory variables, [3 is a k X I vector of parameters and u is
an n X 1 disturbance vector whose components, u, j = 1, ..., n, are
independently normally distributed with means zero and variances
1, ..., n. X is assumed to be of rank k
problem is that of testing the null hypothesis, H0 c2 j1,
., n, against the alternative hypothesis, HA :...u,, where
at least one inequality is a strict inequality.
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