Modelling long memory volatility in the Bitcoin market: Evidence of persistence and structural breaks

• Published date: 01 January 2019
• Author: David Roubaud,Elie Bouri,Rangan Gupta,Luis A. Gil‐Alana
• DOI: http://doi.org/10.1002/ijfe.1670
• Date: 01 January 2019

RESEARCH ARTICLE

Modelling long memory volatility in the Bitcoin market:

Evidence of persistence and structural breaks

Elie Bouri

1

| Luis A. Gil‐Alana

2

| Rangan Gupta

3

| David Roubaud

4

1

USEK Business School, Holy Spirit

University of Kaslik, Jounieh, Lebanon

2

Department of Economicsand Navarra

Center for InternationalDevelopment, ICS,

University of Navarra, Pamplona,Spain

3

Department of Economics, Faculty of

Economics and Management Sciences,

University of Pretoria, Pretoria, South Africa

4

Business School, Montpellier, France

Correspondence

Luis A. Gil‐Alana, University of Navarra,

Pamplona, Spain.

Email: alana@unav.es

Funding information

Ministerio de Economía y Competitividad,

Grant/Award Number: ECO2017‐85503‐R

JEL Classification: C22; G1

Abstract

Motivated by the emergence of Bitcoin as a speculative financial investment,

the purpose of this paper is to examine the persistence in the level and volatil-

ity of Bitcoin price, accounting for the impact of structural breaks. Using para-

metric and semiparametric techniques, we find strong evidence in favour of a

permanency of the shocks and lack of mean reversion in the level series. We

also reveal evidence of structural changes in the dynamics of Bitcoin. After

accounting for the structural breaks in the level series, evidence of mean rever-

sion is uncovered in some cases. Further analyses show evidence of a long

memory in the two measures of volatility (absolute and the squared returns),

whereas some cases of short memory are revealed in the squared returns series

in particular. Practical implications are discussed on the inefficiency in the

Bitcoin market and its importance for Bitcoin users and investors.

KEYWORDS

Bitcoin, long memory, structural breaks

1|INTRODUCTION

The inception of digital currencies or cryptocurrencies,

derived from mathematical cryptography,

1

have attracted

the attention of the media and economic actors. They

represent both a valid form of payment and an

alternative to government‐backed currencies. Among

many cryptocurrencies in existence such as Litecoin,

Ethereum, Ripple, Peercoin, and Dogecoin, Bitcoin in

particular has emerged and taken an increasingly promi-

nent place in the cryptocurrency markets.

Independent whether Bitcoin is regarded as a form of

payment, an alternative or digital form of a currency, or a

financial asset and speculative investment (Bouoiyour &

Selmi, 2015; Bouoiyour, Selmi, & Tiwari, 2015; Yermack,

2015), the literature on the finance of Bitcoin has to be

extended in particular with regards to the analysis of per-

sistence in the level and in the volatility of Bitcoin price.

The aim of this paper is therefore to contribute to the

emerging literature on the economics and finance of

Bitcoin through modelling of persistence in the level

and in the volatility of Bitcoin.

Such an analysis to whether or not long‐term depen-

dence is present in Bitcoin return series could answer a

main question of whether or not the Bitcoin market is

efficient. This is because the presence of long memory

in the high order of Bitcoin series means the statistical

dependence between distant observations of a price series

are not decreasing very rapidly. Therefore, the presence

of persistent dependence between distant Bitcoin obser-

vations represents significant evidence against the effi-

cient market hypothesis or random walk model in the

Bitcoin market. In this sense, conducting such an analysis

is important for Bitcoin users and investors who are both

concerned about managing the risk associated with sharp

Comments from the editor and an anonymous reviewer are gratefully

acknowledged.

1

Dwyer (2015) provides a detailed explanation of the principles of

Bitcoin.

Received: 30 June 2016 Revised: 25 December 2017 Accepted: 8 September 2018

DOI: 10.1002/ijfe.1670

412 © 2018 John Wiley & Sons, Ltd. Int J Fin Econ. 2019;24:412–426.wileyonlinelibrary.com/journal/ijfe