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

Author

Listed:
  • Robin L. Lumsdaine

    (Princeton University)

  • Serena Ng

    (Boston College)

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.

Suggested Citation

  • Robin L. Lumsdaine & Serena Ng, 1998. "Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean," Boston College Working Papers in Economics 370, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:370
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    More about this item

    Keywords

    ARCH; model misspecification; recursive residuals; Lagrange Multiplier test;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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