Long memory and multifractality: a joint test

Enrico Onali*, John Goddard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Early online date3 Feb 2016
Publication statusPublished - 1 Jun 2016

Bibliographical note

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/


  • Exchange rate returns
  • Long memory
  • Multifractality
  • Volatility clustering


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  • Long memory and multifractality: a joint test

    Goddard, J. & Onali, E., Jan 2016, (Unpublished).

    Research output: Preprint or Working paperWorking paper


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