Long memory and multifractality: a joint test

John Goddard, Enrico Onali

Research output: Working paper


The properties of statistical tests for hypotheses concerning the parameters of the multifractal model of asset returns (MMAR) are investigated, using Monte Carlo techniques. We show that, in the presence of multifractality, conventional tests of long memory tend to over-reject the null hypothesis of no long memory. Our test addresses this issue by jointly estimating long memory and multifractality. The estimation and test procedures are applied to exchange rate data for 12 currencies. In 11 cases, the exchange rate returns are accurately described by compounding a NIID series with a multifractal time-deformation process. There is no evidence of long memory.
Original languageEnglish
Publication statusUnpublished - Jan 2016


  • multifractality
  • long memory
  • volatility clustering
  • exchange rate returns

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  • Research Output

    Long memory and multifractality: a joint test

    Onali, E. & Goddard, J., 1 Jun 2016, In : Physica A. 451, p. 288–294 7 p.

    Research output: Contribution to journalArticle

    Open Access
  • Cite this

    Goddard, J., & Onali, E. (2016). Long memory and multifractality: a joint test.