Finite Sample Tests for Arch Effects and Variance Change-points in Linear Regressions

A wide range of tests for heteroskedasticity have been proposed in econometrics and statistics.1 Although a few exact tests are available (e.g. Goldfeld-Quandt’s F -test, its extensions and Szroeter’s procedures),2 common heteroskedasticity tests are asymptotic which may not control size in finite samples. So a number of recent studies have tried to improve the reliability of these tests using Edgeworth, Bartlett, jackknife and bootstrap methods; for references, see Dufour et al. (2001). Yet the latter remain approximate, while Szroeter’s exact tests require computing the distributions of general quadratic forms in normal variables and are seldom used. In this paper, we describe a general solution to the problem of controlling the size of homoskedasticity tests in linear regressions. We exploit the technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963), Dufour and Kiviet (1996, 1998)] to obtain provably exact randomized analogues of the tests considered. This simulation-based procedure yields an exact test when the distribution of the test statistic is pivotal under the null hypothesis: all we need is the possibility of simulating the