Statistical Papers

, Volume 30, Issue 1, pp 105–131 | Cite as

Small sample properties of asymptotically equivalent tests for autoregressive conditional heteroskedasticity

  • Francis X. Diebold
  • Peter Pauly


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.

Key Words

Lagrange multiplier test ARCH Monte Carlo 


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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Francis X. Diebold
    • 1
  • Peter Pauly
    • 2
  1. 1.Special Studies Section Division of Research & StatisticsBoard of Governors Federal Reserve SystemWashington, D.C.
  2. 2.Department of EconomicsUniversity of PennsylvaniaPhila.

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