Maximum entropy autoregressive conditional heteroskedasticity model

Sung Y. Park, Anil K. Bera

Research output: Contribution to journalArticlepeer-review


In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student's t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high peakedness. The ME principle is based on the efficient use of available information, and as is well known, many of the standard family of distributions can be derived from the ME approach. We demonstrate how we can extract information functional from the data in the form of moment functions. We also propose a test procedure for selecting appropriate moment functions. Our procedure is illustrated with an application to the NYSE stock returns. The empirical results reveal that the ME approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively.

Original languageEnglish (US)
Pages (from-to)219-230
Number of pages12
JournalJournal of Econometrics
Issue number2
StatePublished - Jun 2009


  • ARCH models
  • Asymmetry
  • Excess kurtosis
  • Maximum entropy density
  • Peakedness of distribution
  • Stock returns data

ASJC Scopus subject areas

  • Economics and Econometrics


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