Long memory and multifractality: A joint test

John Goddard, Enrico Onali

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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. Among the nested model specifications that are investigated, in 11 out of 12 cases, daily returns are most appropriately characterized by a variant of the MMAR that applies a multifractal time-deformation process to NIID returns. There is no evidence of long memory.
Original languageEnglish
Pages (from-to)288-294
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Early online date03 Feb 2016
Publication statusPublished - 01 Jun 2016
Externally publishedYes


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


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