Abstract

Multifractal processes reproduce some of the stylised features observed in financial time series, namely heavy tails found in asset returns distributions, and long-memory found in volatility. Multifractal scaling cannot be assumed, it should be established; however, this is not a straightforward task, particularly in the presence of heavy tails. We develop an empirical hypothesis test to identify whether a time series is likely to exhibit multifractal scaling in the presence of heavy tails. The test is constructed by comparing estimated scaling functions of financial time series to simulated scaling functions of both an iid Student t-distributed process and a Brownian Motion in Multifractal Time (BMMT), a multifractal processes constructed in Mandelbrot et al. (1997). Concavity measures of the respective scaling functions are estimated, and it is observed that the concavity measures form different distributions which allow us to construct a hypothesis test. We apply this method to test for multifractal scaling across several financial time series including Bitcoin. We observe that multifractal scaling cannot be ruled out for Bitcoin or the Nasdaq Composite Index, both technology driven assets.

Highlights

  • The cryptocurrency market is an emerging market comprised of thousands of digital assets including Bitcoin

  • We address the central research question: Do Bitcoin prices exhibit multifractal scaling? To answer this question, we investigate the effect of heavy-tails on the scaling function and study scenarios in which false positive1 detection occurs

  • We explore the possible range of behaviours for scaling functions for simulated multifractal processes

Read more

Summary

Introduction

The cryptocurrency market is an emerging market comprised of thousands of digital assets including Bitcoin. Sly (2006) and Grahovac and Leonenko (2014) demonstrate that attempts to use the scaling function to detect multifractality may mistakenly give rise to false positive results, due to heavy-tailed effects. This calls into question the reliability of the above-mentioned results.

Methods
Results
Conclusion

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.