The exponential growth of BitCoin and other cryptocurrencies is a phenomenon that has attracted considerable attention in recent years. The cryptocurrency market is rather young (BitCoin was created in 2009, but active trade only started in 2013) and therefore still mostly unexplored (see Caporale and Plastun, 2017 for one of the very few existing studies, with a focus on calendar anomalies). One of the key issues yet to be analysed is whether the dynamic behaviour of cryptocurrencies is predictable, which would be inconsistent with the Efficient Market Hypothesis (EMH), according to which prices should follow a random walk (see Fama, 1970). Long-memory techniques can be applied for this purpose. Several studies have provided evidence of persistence in asset price dynamics (see Greene and Fielitz, 1977; Caporale et al., 2016), and also found that this changes over time (see Lo, 1991), but virtually none has focused on the cryptocurrency market. One of the few exceptions is due to Bouri et al. (2016), who find lon- memory properties in the volatility of Bitcoin.
As already mentioned above, the cryptocurrency market has only been in existence for a few years, and therefore only a handful of studies have been carried out. ElBahrawy et al. (2017) provide a comprehensive analysis of 1469 cryptocurrencies considering various issues such as market shares and turnover. Cheung et al. (2015), Dwyer (2014), Bouoiyour and Selmi (2015) and Carrick (2016) show that this market is much more volatile than others. Halaburda and Gandal (2014) analyse its degree of competitiveness Urquhart (2016) and Bartos (2015) focus on efficiency finding evidence for and against respectively. Anomalies in the cryptocurrency market are examined by Kurihara and Fukushima (2017) and Caporale and Plastun (2017).
Bariviera et al. (2017) test the presence of long memory in the Bitcoin series from 2011 to 2017. They find that the Hurst exponent changes significantly during the first years of existence of Bitcoin before becoming more stable in recent times. Bariviera (2017) also use the Hurst exponent and detect long memory in the daily dynamics of BitCoin as well as its volatility; in addition, they find more evidence of informational efficiency since 2014. Bouri et al. (2016) examine persistence in the level and volatility of Bitcoin using both parametric and semiparametric techniques; they detect long memory in both measures of volatility considered (absolute and squared returns). Catania and Grassi (2017) provide further evidence of long memory in the cryptocurrency market, whilst Urquhart (2016) using the R/S Hurst exponent obtains strong evidence of anti-persistence, which indicates non-randomness of Bitcoin returns.