Specification test for a linear regression model with ARCH process

Anil K. Bera, Xiao Lei Zuo

Research output: Contribution to journalArticlepeer-review


ARCH models are used widely in analyzing economic and financial time series data. Many tests are available to detect the presence of ARCH; however, there is no acceptable procedure available for testing an estimated ARCH model.. In this paper we develop a test for a linear regression model with ARCH disturbances using the framework of the information matrix (IM) test. For the ARCH specification, the covariance matrix of the indicator vector is not block diagonal, and the IM test is turned out to be a test for variation in the fourth moment, i.e., a test for heterokurtosis. An illustrative example is provided to demonstrate the usefulness of the proposed test.

Original languageEnglish (US)
Pages (from-to)283-308
Number of pages26
JournalJournal of Statistical Planning and Inference
Issue number2
StatePublished - Mar 1 1996


  • Autoregressive conditional heteroskedasticity
  • Double length regression
  • Information matrix test

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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