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Statistical Tests of Distributional Scaling Properties for Financial Return Series

Hallam, Mark and Olmo, Jose (2018) 'Statistical Tests of Distributional Scaling Properties for Financial Return Series.' Quantitative Finance, 18 (7). 1211 - 1232. ISSN 1469-7688

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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.

Item Type: Article
Uncontrolled Keywords: Multifractal, Unifractal, Bootstrap inference, Hypothesis testing, Financial returns
Subjects: H Social Sciences > HA Statistics
H Social Sciences > HG Finance
Divisions: Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Essex Finance Centre
Depositing User: Mark Hallam
Date Deposited: 06 Mar 2017 12:52
Last Modified: 29 Jan 2020 12:15
URI: http://repository.essex.ac.uk/id/eprint/19203

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