Small sample properties of asymptotically equivalent tests for autoregressive conditional heteroskedasticity

Models that allow for autoregressive conditional heteroskedasticity (ARCH) in the error process have recently found widespread application. The purpose of this paper is to evaluate, through Monte Carlo analysis, the small sample properties of an exact Lagrange multiplier test for the presence of ARCH, and to compare the power of this test with that of an asymptotically equivalent TR² version. The comparison involves first-and higher-order variants of these processes. The results indicate substantial power differentials in favor of the exact LM test, by up to 15% for sample sizes smaller than 100.