Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean

Robin Lumsdaine and Serena Ng ()
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Robin Lumsdaine: Princeton University

No 370, Boston College Working Papers in Economics from Boston College Department of Economics

Abstract: 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 T times the R^2 from a regression of squared residuals on p of its lags. This test has been shown to have a Lagrange multiplier interpretation and is asymptotically distributed as a Chi^2(p) random variable. Underlying this test is the assumption of a correctly specified conditional mean. In this paper, we consider the properties of the ARCH test when there is a possibly misspecified conditional mean. Examples of misspecification include omitted variables, structural change, and parameter instability. We show that misspecification will lead to overrejection of the null of conditional homoskedasticity. We demonstrate the use of recursive residuals to improve the fit of a first stage conditional mean regression. We illustrate these results via Monte Carlo simulation and consider two empirical examples.

Keywords: ARCH; model misspecification; recursive residuals; Lagrange Multiplier test (search for similar items in EconPapers)
JEL-codes: C22 C52 (search for similar items in EconPapers)
Pages: 24 pages
Date: 1998-08-27
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Journal Article: Testing for ARCH in the presence of a possibly misspecified conditional mean (1999)
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