Skip to main content

Research Repository

Advanced Search

Long memory and multifractality: a joint test

Goddard, John; Onali, Enrico

Long memory and multifractality: a joint test Thumbnail


John Goddard

Enrico Onali


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.

Previous article in issue


Goddard, J., & Onali, E. (2016). Long memory and multifractality: a joint test. Physica A: Statistical Mechanics and its Applications, 451,

Journal Article Type Article
Acceptance Date Dec 6, 2015
Online Publication Date Feb 3, 2016
Publication Date Jun 1, 2016
Deposit Date Jun 19, 2018
Publicly Available Date Jun 19, 2018
Journal Physica A: Statistical Mechanics and its Applications
Print ISSN 0378-4371
Electronic ISSN 0378-4371
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 451
Keywords Multifractality; Long memory; Volatility clustering;
Exchange rate returns
Public URL
Publisher URL


long memory and multifractality.pdf (587 Kb)

NA - Not Applicable (or Unknown)

Downloadable Citations