Testing for ARCH in the presence of a possibly misspeci"ed conditional mean
نویسندگان
چکیده
Ever since the development of the Autoregressive Conditional Heteroskedasticity (ARCH) model (Engle, 1982), testing for the presence of ARCH has become a routine diagnostic. One popular method of testing for ARCH is 1 times the R2 from a regression of the squared residuals on p of its lags. This test has been shown to have a lagrange multiplier interpretation and is asymptotically distributed as a s2(p) random variable. Underlying this test is the assumption of a correctly speci"ed conditional mean. In this paper, we consider the properties of the ARCH test when there is a possibly misspeci"ed conditional mean. Examples of misspeci"cation include omitted variables, structural change, and parameter instability. We show that, in general, misspeci"cation will lead to overrejection of the null hypothesis of conditional homoskedasticity. We demonstrate the use of recursive residuals to improve the "t of a "rst-stage conditional mean regression. We illustrate these results via Monte Carlo simulations and consider two empirical examples. ( 1999 Elsevier Science S.A. All rights reserved. JEL classixcation: C22; C52
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