Multifractal Detrended Fluctuation Analysis of Return on Bitcoin*

• Published date: 01 March 2021
• Author: Keshab Shrestha
• Date: 01 March 2021
• DOI: http://doi.org/10.1111/irfi.12256

Multifractal Detrended Fluctuation

Analysis of Return on Bitcoin*

KESHAB SHRESTHA

School of Business, Monash University Malaysia, Bandar Sunway, Malaysia

ABSTRACT

We revisit the issue of market efficiency of Bitcoin, which is an important part

of the new financial technology (FinTech), by analyzing the Bitcoin returns

using two recently developed analytical techniques called bipower variation

method and Multifractal Detrended Fluctuation Analysis (MF-DFA). MF-DFA

allows us to analyze the return series in ways not possible using a monofractal

analytical techniques such as detrended fluctuation analysis (DFA) and R/S

method. The bipower variation method suggests that the Bitcoin returns are

efficient and contain some large finite jumps. Using MF-DFA, we find that the

Bitcoin returns are multifractal and, therefore, the Bitcoin market is not effi-

cient. By carrying out further analysis, we also find that the multifractility and

inefficiency are causedby the autocorrelated returns as well as extremereturns.

JEL Codes: G12; G14

Accepted: 31 January 2019

I. INTRODUCTION

Bitcoin is a digital currency or cryptocurrency, an important part of the new

financial technology (FinTech), which has attracted significant interests from

academicians, practitioners as well as policy makers. This is partly due to the

phenomenal rise in its value as well as increasing acceptability. According to the

data from Thomson Reuters (Datastream), Bitcoin closed at $18,940.57 on

December 18, 2017, whereas the closing price on August 18, 2011 was $10.90.

The significance of Bitcoin increased even further, when the Chicago Board

Options Exchange started trading Bitcoin futures on December 10, 2017. A week

later, the Chicago Mercantile Exchange, the world’s largest futures exchange,

also started trading Bitcoin futures with different contract size. Therefore, it

would be of significant interest to academicians, practitioners, and policy makers

to find if the Bitcoin prices are efficient within the meaning of Fama (1970).

Recently, Urquhart (2016) used a set of tests on Bitcoin returns aimed at testing

zero autocorrelations, unit roots, nonlinearities, and long range dependence. He

finds the Bitcoin returns to be significantly inefficient for the full sample (August

1, 2010 to July 31, 2016). However, when the sample is split into two subsample

* I would like to thank School of Business, Monash University Malaysia for research support.

I would also like to thank the anonymous reviewer for important comments and suggestions.

© 2019 International Review of Finance Ltd. 2019

International Review of Finance, 21:1, 2021: pp. 312–323

DOI: 10.1111/irfi.12256