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Statistical tests of distributional scaling properties for financial return series

Statistical tests of distributional scaling properties for financial return series
Statistical tests of distributional scaling properties for financial return series
Existing empirical evidence of distributional scaling in financial returns has helped motivate the use of multifractal processes for modelling return processes. However, this evidence has relied on informal tests that may be unable to reliably distinguish multifractal processes from other related classes. The current paper develops a formal statistical testing procedure for determining which class of fractal process is most consistent with the distributional scaling properties in a given sample of data. Our testing methodology consists of a set of test statistics, together with a model based bootstrap resampling scheme to obtain sample p-values. We demonstrate in Monte Carlo exercises that the proposed testing methodology performs well in a wide range of testing environments relevant for financial applications. Finally, the methodology is applied to study the scaling properties of a dataset of intraday equity index and exchange rate returns. The empirical results suggest that the scaling properties of these return series may be inconsistent with purely multifractal processes
Multifractal, Unifractal, Bootstrap inference, Hypothesis testing, Financial returns
1469-7688
Hallam, Mark
90b75cfc-3890-4567-be1a-075069235129
Olmo, Jose
706f68c8-f991-4959-8245-6657a591056e
Hallam, Mark
90b75cfc-3890-4567-be1a-075069235129
Olmo, Jose
706f68c8-f991-4959-8245-6657a591056e

Hallam, Mark and Olmo, Jose (2018) Statistical tests of distributional scaling properties for financial return series. Quantitative Finance. (doi:10.1080/14697688.2017.1298832).

Record type: Article

Abstract

Existing empirical evidence of distributional scaling in financial returns has helped motivate the use of multifractal processes for modelling return processes. However, this evidence has relied on informal tests that may be unable to reliably distinguish multifractal processes from other related classes. The current paper develops a formal statistical testing procedure for determining which class of fractal process is most consistent with the distributional scaling properties in a given sample of data. Our testing methodology consists of a set of test statistics, together with a model based bootstrap resampling scheme to obtain sample p-values. We demonstrate in Monte Carlo exercises that the proposed testing methodology performs well in a wide range of testing environments relevant for financial applications. Finally, the methodology is applied to study the scaling properties of a dataset of intraday equity index and exchange rate returns. The empirical results suggest that the scaling properties of these return series may be inconsistent with purely multifractal processes

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More information

Accepted/In Press date: 17 February 2017
e-pub ahead of print date: 13 February 2018
Keywords: Multifractal, Unifractal, Bootstrap inference, Hypothesis testing, Financial returns
Organisations: Economics, Southampton Marine & Maritime Institute

Identifiers

Local EPrints ID: 411635
URI: http://eprints.soton.ac.uk/id/eprint/411635
ISSN: 1469-7688
PURE UUID: 953172ee-9295-4abb-a343-75e2be9738d7
ORCID for Jose Olmo: ORCID iD orcid.org/0000-0002-0437-7812

Catalogue record

Date deposited: 21 Jun 2017 16:32
Last modified: 07 Oct 2020 06:21

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