Simulation-based Finite-sample Tests for Heteroskedasticity and ARCH Effects

• Activity Number: 176
• Type: Contributed
• Date/Time: Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Lynda Khalaf*+ and Jean-Marie Dufour and Jean-Thomas Bernard and Ian Genest
• Affiliation(s): Université Laval and Université de Montréal and Université Laval and Université Laval
• Keywords: heteroskedasticity ; linear regression ; Monte Carlo test ; exact test ; structural stability ; (G)ARCH test

Abstract

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.