Simulation-based finite-sample tests for heteroskedasticity and ARCH effects

Tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations. We show that the size of such tests can be perfectly controlled in finite samples through Monte Carlo test techniques, with both Gaussian and non-Gaussian (heavy-tailed) disturbance distributions. The procedures studied include standard heteroskedasticity tests [e.g., Glejser, Bartlett, Cochran, Hartley, Breusch–Pagan–Godfrey, White, Szroeter] as well as tests for ARCH-type heteroskedasticity. Sup-type and combined tests are also proposed to allow for unknown breakpoints in the variance. The fact that the proposed procedures achieve size control and have good power is demonstrated in a Monte Carlo simulation.