Forecasting the volatility of Bitcoin: The importance of jumps and structural breaks

• Published date: 01 November 2020
• Author: Dehua Shen,Andrew Urquhart,Pengfei Wang
• Date: 01 November 2020
• DOI: http://doi.org/10.1111/eufm.12254

Eur Financ Manag. 2020;26:1294–1323.wileyonlinelibrary.com/journal/eufm1294

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© 2019 John Wiley & Sons Ltd.

DOI: 10.1111/eufm.12254

ORIGINAL ARTICLE

Forecasting the volatility of Bitcoin: The

importance of jumps and structural breaks

Dehua Shen

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Andrew Urquhart

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Pengfei Wang

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1

College of Management and Economics,

Tianjin University, Tianjin, China

2

ICMA Centre, Henley Business School,

University of Reading, Reading, UK

Correspondence

Pengfei Wang, College of Management

and Economics, Tianjin University, 92

Weijin Road, Tianjin 300072, China.

Email: pengfeiwang@tju.edu.cn

Abstract

This paper studies the volatility of Bitcoin and deter-

mines the importance of jumps and structural breaks in

forecasting volatility. We show the importance of the

decomposition of realized variance in the in‐sample

regressions using 18 competing heterogeneous autore-

gressive (HAR) models. In the out‐of‐sample setting, we

find that the HARQ‐F‐J model is the superior model,

indicating the importance of the temporal variation and

squared jump components at different time horizons.

We also show that HAR models with structural breaks

outperform models without structural breaks across all

forecasting horizons. Our results are robust to an

alternative jump estimator and estimation method.

KEYWORDS

bitcoin, jumps, realized volatility, structural breaks, volatility

forecasting

JEL CLASSIFICATION

C53, G15, G17

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INTRODUCTION

Bitcoin has received a great deal of attention since it was first proposed by Nakamoto (2008), and this

attention has come from the media, governments, regulators, as well as from investors, who have

been attracted to Bitcoin by its huge increase in price during 2017. However, this surge in price has

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We wish to thank John Doukas (the Editor) and an anonymous referee for their insightful and constructive suggestions.

We are grateful to Chardin Wese Simen for his valuable comments on earlier versions of this paper. This work is

supported by the National Natural Science Foundation of China (71701150, 71790594, and U1811462). Any remaining

errors are our own.

been accompanied by huge volatility and uncertainty regarding the future price path of this popular

cryptocurrency. There is growing evidence that Bitcoin offers substantial diversification to investors

when included in portfolios (Kajtazi & Moro, 2019; Platanakis & Urquhart, 2019) and that technical

trading rules generate significant returns to investors (Hudson & Urquhart, 2019). Therefore,

forecasting the volatility of Bitcoin is of great interest, and this paper provides a comprehensive

overview of the forecasting ability of various time‐series models derived from the innovative

heterogeneous autoregressive (HAR) specificationofCorsi(2009).Weconsider18HARmodels,and

the analysis is conducted in sample, and, more importantly, out of sample for Bitcoin from January

2012 to September 2018. Our results show that the inclusion of jumps is important when forecasting

Bitcoin volatility at all forecasting horizons. Specifically, we find that the HARQ‐F‐J model provides

the best out‐of‐sample forecast of volatility for a 1‐day horizon, indicating the importance of the

temporal variation and squared jump components at different horizons. For the 1‐week and 1‐month

forecast horizons, we find that a number of models that include jumps are superior to models without

jumps. Also, we find that the inclusion of structural breaks in each HAR model improves the

forecasting ability of these models when considering forecast horizons of 1 day, 1 week, and 1 month.

Therefore, our results indicate the importance of the temporal variation and squared jump

components, separated at different horizons, as well as structural breaks, in forecasting Bitcoin

volatility through competing HAR models.

Since the availability of high‐frequency data has become more common, there is ample evidence of

the economic value of forecasting volatility using intraday data. Most studies find that simple

autoregressive structures such as HAR models provide much better forecasting ability than

generalized autoregressive conditional heteroskedasticity (GARCH)‐type models that employ daily

data (see, for instance, Andersen & Bollerslev, 1997, 1998; Andersen, Bollerslev, Diebold, & Ebens,

2001; Andersen, Bollerslev, Diebold, & Labys, 2003; Giot & Laurent, 2007; Koopman, Jungbacker, &

Hol, 2005).

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This improvement comes from the fact that GARCH models employ daily data while

HAR models are able to capture more information contained in intraday data.

The literature on cryptocurrencies is growing, with many papers reporting the inefficiency of

Bitcoin (Khuntia & Pattanayak, 2018; Urquhart, 2016; Nadarajah and Chu, 2017; Tiwari, Jana, Das, &

Roubaud, 2018), the hedging and diversification benefits (Borri, 2019; Bouri, Molnár, Azzi, Roubaud,

& Hagfors, 2017; Corbet, Meegan, Larkin, Lucey, & Yarovaya, 2018; Urquhart & Zhang, 2018), the

existenceofbubbles(Cheah&Fry,2015;Corbet,Lucey,&Yarovaya,2018),investorattention(Shen,

Urquhart, & Wang, 2019; Urquhart, 2018), and the behavior of Bitcoin returns (Corbet & Katsiampa,

2018; Phillip, Chen, & Peiris, 2018; Urquhart, 2017; Katsiampa, 2018).

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However, there is limited

literature examining the volatility dynamics of Bitcoin, with Katsiampa (2017) the first to explore the

optimal conditional heteroskedasticity model with regard to goodness of fit to Bitcoin and finding that

an autoregressive component GARCH (AR‐CGARCH) model is the most appropriate, indicating both

the short‐and long‐run component of the conditional variance. Chaim and Laurini (2018) show that

jumps in volatility are permanent in Bitcoin, while jumps in returns are contemporaneous. They also

show that large jumps in mean returns are all negative and associated with hacks and forks. Catania,

Grassi, and Ravazzolo (2019) compare the abilities of several alternative univariate and multivariate

models to predictor cryptocurrencies and show large, statistically significant improvements in the

point forecasting of Bitcoin when using combinations of univariate models, while Katsiampa, Corbet,

and Lucey (2019) show strong interdependencies between cryptocurrency volatilities and that time‐

varying conditional correlations of volatility exist between cryptocurrencies. Gronwald (2019) shows

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Andersen, Bollerslev, Christoffersen, and Diebold (2006) provides an excellent survey.

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See Corbet, Lucey, Urquhart, and Yarovaya (2019) for a recent review of the empirical literature on cryptocurrencies.

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