Elsevier

Finance Research Letters

Volume 29, June 2019, Pages 222-230
Finance Research Letters

Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum

https://doi.org/10.1016/j.frl.2018.07.011Get rights and content

Highlights

  • We examine structural break impacts on the dual long memory of Bitcoin and Ethereum.

  • We use four different ARFIMA-GARCH family models.

  • Dual long memory exists in Bitcoin and Ethereum returns and volatility.

  • Persistence decreases after considering long memory and switching states.

  • The FIGARCH with structural breaks is the most suitable for volatility forecasting.

Abstract

This study explores the impacts of structural breaks (SB) on the dual long memory levels of Bitcoin and Ethereum price returns. We identify dual long memory and structural changes on cryptocurrency markets using four different generalized autoregressive conditional heteroskedasticity models (e.g., GARCH, FIGARCH, FIAPARCH, and HYGARCH). Furthermore, the persistence level of both returns and volatility decreases after accounting for long memory and switching states. Finally, the FIGARCH model with SB variables provides a comparatively superior forecasting accuracy performance. These findings have significant implications for both cryptocurrency allocations and portfolio management.

Introduction

Long memory (LM) and structural breaks (SB) are two important elements in modeling financial time series (Granger and Joyeux, 1980, Hosking, 1981, Mandelbrot and Van Ness, 1968), providing appropriate asset allocation and averting the losses and damages induced by extreme volatility, which affects investors’ expectations of future stock prices and, consequently, market efficiency. Burton (1987) argues that, if the market does not exhibit LM, yesterday's events will not affect today's prices. Investors and portfolio managers may thus avoid future losses by considering how SB and LM impact future volatilities, as these two major stylized facts can improve the volatility prediction of asset prices and be included in the volatility model through an out-of-sample forecasting analysis to select the best model for volatility forecasting, which has implications in the assessment of investment risks, asset valuation, and risk management. Mensi et al. (2015) argue the marginalization of SB on the market can lead to sizeable upward biases in the volatility persistence level because it changes expectations and arbitrage activities. The literature concludes most investors are under the pressure of market events (LM and SB). As such, investors and traders may trade and take risks without paying attention to Bitcoin market information regarding LM and SB.

Bitcoin (BTC) has been attracting significant attention since its creation in 2009, and its market experienced high instability during the past few years (increasing phases followed by decreasing ones). Bitcoin is an electronic payment system (Nakamoto, 2008) and the largest cryptocurrency in terms of market capitalization at above 80% of the cryptocurrency capitalization in 2016 (Al-Yahyaee et al., 2018). There is a growing empirical literature on Bitcoin, addressing efficiency, long memory, multifractality, and price discovery. Unlike other cryptocurrencies, Ethereum (ETH) attracted significant attention as well, reflected in its market capitalization as it ranks second among more than one hundred cryptocurrencies (see https://coinmarketcap.com/). It uses blockchain technology and has the potential to be a “World Computer.” Ethereum is a decentralized platform and runs smart contracts.

Urquhart (2016) tests the market efficiency hypothesis of Bitcoin using different models (Ljung–Box test, Runs test, Bartels test, AVR test, BDS test, and R/S Hurst), showing Bitcoin is an inefficient market, an inefficiency that decreases over time and moves towards an efficient market. More recently, Urquhart (2018) analyzes the key factors that have driven Bitcoin using Google Trends data. Urquhart (2018) shows evidence that realized volatility and volume are determinant factors of next day investor attention. Corbet et al. (2017) examine the existence pricing discovery and internal fundamental explanatory variables in two major cryptocurrencies, namely Bitcoin and Ethereum cryptocurrencies. The authors show there are periods of clear bubble behavior and Bitcoin now is in a bubble phase (i.e., price increases above USD 1,000). Using the time domain analysis of Barunik and Krehlik, 2015, Corbet et al., 2018 investigate the relationships between three major cryptocurrencies (Bitcoin, Ripple, and Litecoin) and a set of financial assets (MSC GSCI Total Returns Index, USD Broad Exchange Rate, S&P 500 Index, COMEX closing gold price, volatility index, and Markit ITTR110 index), showing the relative isolation of Bitcoin, Ripple, and Litecoin assets from classical financial and economic assets. With short investment horizons, these three cryptocurrencies provide diversification advantages for investors.

Dyhrberg (2016a) uses the standard GARCH and exponential GARCH (EGARCH) models to analyze whether Bitcoin experiences financial asset capabilities and finds several similarities to the gold and dollar markets. This result reveals hedging capabilities and advantages as an exchange medium. The EGARCH model results support that Bitcoin is a hedge asset against extreme negative movement prices. Using the same methodology, Dyhrberg (2016b) finds Bitcoin is a hedge asset against stocks. Al-Yahyaee et al. (2018) use the Multifractal Detrended Fluctuation. Analysis (MF-DFA) approach to test multifractality and the efficiency of Bitcoin compared to gold, stock, and foreign exchange markets. The authors conclude Bitcoin shows strong long memory and multifractality properties compared to other financial assets.

Bariviera (2017) uses the Hurst exponent method to study the long memory behavior of Bitcoin and identifies long memory in volatility for 2011–2017. Using the same methodology and both daily and intraday prices, Bariviera et al. (2017) analyze the long memory features of Bitcoin returns, as well as EUR and GBP exchange rates, finding no relationship between liquidity and long memory dependence. More recently, Thies and Molnár (2018) investigate the presence of SB in Bitcoin returns and return volatility using the Bayesian change point model. They show evidence of SB in Bitcoin returns and volatility and different positive average returns regimes and one negative average return regime.

The literature (see, e.g., Aggarwal et al., 1999, Lamoureux and Lastrapes, 1990, Lastrapes, 1989) on structural changes concludes SB should be taken into account when modeling conditional volatility, otherwise possibly causing spurious estimation of volatility persistence. Consequently, this study sheds light on the impacts of SB and dual LM on the conditional mean and volatility of the two largest cryptocurrency markets—Bitcoin and Ethereum—using different GARCH models. As a complex and chaotic structure characterizes this digital market, it is important to consider nonlinear models to address this matter. To the best of our knowledge, this is the first study that addresses the dual long memory and SB of Bitcoin and Ethereum, as all previous studies address only the LM in terms of variance and ignore the LM for means as well as SB variables, which is crucial for portfolio design. Further, to measure forecasting accuracy, we carry an out-of-sample analysis under different time horizons using the mean of square errors (MSE) and the mean of absolute errors (MSE) of volatility. We also apply the Diebold and Mariano (1995) test for robustness.

Empirically, we consider at least four GARCH models crucial for understanding and forecasting volatility. These models have different usefulness for investigating portfolio risk. Specifically, the GARCH model developed by Bollerslev (1986) is a benchmark and extends the ARCH model of Engle (1982) by considering the previous conditional volatility in the model. The fractionally integrated GARCH (FIGARCH) model of Baillie et al. (1996) outperforms the simple GARCH model by considering one important stylized fact, namely the long-range memory, which is important for asset allocation and portfolio management. The fractionally integrated asymmetric power ARCH (FIAPARCH) model of Tse (1998) is an extension of the FIGARCH model and it counts, in addition to the long-range memory behavior, the asymmetric facts in the conditional variance or leverage effects (i.e., bad news and good news have different impacts on conditional volatility). Finally, the hyperbolic GARCH (HYGARCH) model proposed by Davidson (2004) has infinite variance.

Our results show different regime states and dual LM on the Bitcoin and Ethereum markets and that the persistence level decreases in both mean and variance after accounting for a high volatility regime. The out-of-sample analysis shows the FIGARCH model with SB variables is the most suitable for accurate volatility forecasting results compared to the other models. This result could help investors exploit Bitcoin and Ethereum by predicting their future prices and managing Bitcoin and Ethereum portfolios in the best possible way.

The remainder of this paper is organized as follows: Section 2 explains dual long memory methods, Section 3 describes data and descriptive statistics and discusses the empirical results, and Section 4 concludes the paper.

Section snippets

GARCH family models

The autoregressive fractional integral moving average (ARFIMA) model is a well-known parametric tool for testing long memory characteristics of the conditional mean, referred as the fractionally integrated process I(d ) in the conditional mean. We consider the ARFIMA(p,d,q) model:Ψ(L)(1L)ξ(ytμ)=Θ(L)εtεt=ztσt,where εt is assumed to be identically and independently distributed, with variance σt2 and innovations {zt}, following a Student's t distribution (ztST(0, 1, v)).1

Data and summary statistics

We consider daily spot prices of Bitcoin (Ethereum) from July 1, 2011 (August 9, 2015 for ETH) to March 3, 2018. The data are sourced from the Coindesk Price Index website for both Bitcoin and Ethereum. Fig. 1 shows the quarterly average trading volumes and market capitalizations of the two cryptocurrencies (from https://coinmarketcap.com/), where the market capitalization and trading volume for both cryptocurrencies show a spectacular growth in 2018 compared to 2014. In 2018 Q1, the Bitcoin

Conclusions

This paper first explores the impact of dual LM and SB on the conditional volatility of Bitcoin and Ethereum markets. We use four competing GARCH models, namely ARFIMA-GARCH, ARFIMA-FIGARCH, ARFIMA-FIAPARCH, and ARFIMA-HYGARCH. Our results show the dual long memory property of Bitcoin and Ethereum, contrasting the market efficiency and random walk hypothesis. Additionally, Bitcoin presents different regimes (high and low). After accounting for SB, we find long memory in the mean and variance

Acknowledgement

The last author (Sang Hoon Kang) acknowledges receiving financial support from the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2017S1A5B8057488).

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