ARCH and bilinearity as competing models for nonlinear dependence

Anil K. Bera, Matthew L. Higgins

Research output: Contribution to journalArticlepeer-review


In this article we consider whether the wide acceptance of autoregressive conditional heteroscedasticity (ARCH) models may be at the expense of other nonlinear processes, such as bilinear models. We first propose a joint test for ARCH and bilinearity. A nonnested test is then suggested to determine whether nonlinear dependence should be attributed to ARCH or bilinearity. The tests are then applied to three series. When generalized ARCH (GARCH) models are taken as the null hypothesis, we fail to reject it for all the data series. When bilinearity is taken as the null, however, it is rejected in two cases. Moreover, an out-of-sample forecasting exercise shows that the GARCH model is superior. The results, therefore, indicate a strong preference for the GARCH model.

Original languageEnglish (US)
Pages (from-to)43-50
Number of pages8
JournalJournal of Business and Economic Statistics
Issue number1
StatePublished - Jan 1997


  • Autoregressive conditional heteroscedasticity
  • Cox test
  • Nonnested models
  • Out-of-sample forecasts
  • Simulation approach

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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