Abstract:
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We describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics 9the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria0 as well as tests for ARCH-type models. We also suggest several extensions of the existing procedures (sup-type or combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values. We show that the MC test procedure conveniently solves the intractable null distribution problem, e.g. those raised by the sup-type and combined test statistics as well as unidentified nuisance parameter problems. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on: 1.) (G)ARCH alternatives; 2.) the case where the variance increases monotonically with one exogenous variable or the mean of the dependent variable; 3.) breaks-in-variance at possibly unknown points.
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