Intraday downward/upward multifractality and long memory in Bitcoin and Ethereum markets: An asymmetric multifractal detrended fluctuation analysis☆
Introduction
Multifractality is a major stylized fact in financial time series. The source of multifractality is known to be the long-range memory and fat tails in the return distribution (Baruník et al., 2012, Green et al., 2014). This implies that financial time series with high multifractality show sharp rises and drops, the volatility of price movements is clustering, and the price dynamics follow a pattern and have a certain predictability. Moreover, the multifractal behaviour in international financial markets may be time-varying, and differ in upside and downside market conditions; if this be the case, investment risk may also be time-varying, and price movements show asymmetric responses to good or bad market news. Thus, changes in multifractality and efficiency have important implications vis-à-vis asset allocations and portfolio management.
The multifractality of equity prices closely relates to the long-memory feature of the market, and it contradicts the efficiency market hypothesis (EMH) in finance theory. On the other hand, asymmetric correlations between financial assets have implications on asset allocations and portfolio risk assessment, on account of asymmetric risk imposed by market conditions or the upward or downward movement of asset prices. Thus, enhancing the general understanding of multifractal behaviour and time-varying efficiency in financial markets helps market participants optimize their investment decision-making process. Additionally, policy-makers are interested in handling these stylized facts, as they may inform the stimulation of economic development: by better understanding these facts, they may craft new policy that enhances the efficiency of the financial market and optimizes resource allocations.
Since their creation in 2008, cryptocurrencies—in particular, Bitcoin (BTC) and Ethereum (ETH)—have attracted special attention. More than 100 cryptocurrencies are traded in the market, but BTC and ETH remain the most widely traded ones: together they account for more than 60% of the total cryptocurrency market capitalization. Due to their exponentially increasing popularity, an emerging body of literature has addressed the cryptocurrency market. For example, a first strand of research analyses the informational efficiency of Bitcoin, and finds that Bitcoin is inefficient (Urquhart, 2016, Nadarajah and Chu, 2017, Cheah et al., 2018, Al-Yahyaee et al., 2018, Tiwari et al., 2018, Vidal-Tomás and Ibañez, 2018). Some studies investigate other cryptocurrency market features (Koutmos, 2018, Katsiampa, 2018, Chaim and Laurini, 2018).
The current study aims to examine the asymmetric multifractality and dynamic market efficiency of the world's two largest cryptocurrencies in terms of market capitalization, BTC and ETH. To do this, we use the generalized Hurst exponent and the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) approach with high-frequency data (5, 10, and 15 min). The advantage inherent in the A-MF-DFA method of Cao et al. (2013) is that it discerns the scaling properties in two different market trends; uptrends and downtrends. We thus acquire considerable information on asset allocation when we consider separately the upward and downward market movements. More precisely, the portfolio gains are maximized when the market goes up, and the portfolio loss is reduced when the market goes down. Thus, addressing the price movements during two different market situations is important to understanding the persistence of prices in cryptocurrency markets. We follow Lee et al. (2018) and quantify the generalized Hurst exponent by simultaneously discerning the overall long-range correlation for overall trends, uptrends, and downtrends; this procedure allows us to analyse the asymmetric EMH by exploring the differences among the various trends in terms of the asymmetric generalized Hurst exponent. To the best of our knowledge, the current study is the first to use the A-MF-DFA to investigate the intraday dynamics of BTC and ETH prices for overall, upward, and downside trends.
Our results provide evidence of asymmetric multifractality for upward and downward BTC and ETH markets. The ETH market is less inefficient than that of the BTC, regardless of the frequency of the overall, upward, and downward trends. Finally, we find that the inefficiency is lower when the BTC and ETH markets follow an upward movement (save for the upward ETH with the 15-min frequency). Investors should consider the upward and downward trends when forecasting BTC and ETH prices. The ability to ‘beat’ these markets and generate abnormal returns is more evident in downward market conditions. In addition, investors and portfolio managers can leverage asymmetric multifractality to forecast future prices and generate profits.
Section snippets
Data and methodology
The current study investigates two major cryptocurrency markets, BTC and ETH. We use the closing price derived from high-frequency intraday data obtained from the Bitfinex Exchange, at three different frequencies (i.e. 5, 10, and 15 min). The sample data of the BTC (ETH) spans the period from June 1, 2013 (June 1, 2016) to June 23, 2018. Returns are calculated by taking the difference in the logarithm of two consecutive prices.
The current study leverages the A-MF-DFA method. By using this
Asymmetric multifractality analysis results
Fig. 1 presents the asymmetric MF-DFA functions Fq(n) versus the time scale n in a log-log plot of the BTC and ETH returns. The asymmetry in the fluctuation function is discovered within a single unit of the time scale, where the distinctions between the uptrend and downtrend values are observed throughout most of the time scale. As seen in this figure, the trajectories for the asymmetric MF-DFA functions Fq(n) versus the time scale n for different frequencies are similar. The A-MF-DFA discerns
Conclusion
This study leveraged intraday data at three different frequencies (5, 10, and 15 min) and the asymmetric multifractal detrended fluctuation analysis approach to examine asymmetric multifractality, long-range memory, and time-varying efficiency for overall, downside, and upside trends in the price dynamics of the world's two largest cryptocurrencies (i.e. BTC and ETH).
We found evidence of multifractality in the movement of cryptocurrency prices, implying that these prices do not follow a random
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This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2017S1A5B8057488).