**5. Conclusions**

We provided the first analysis for detecting bull and bear markets for the three largest cryptocurrencies of Bitcoin, Ethereum, and Litecoin in high-frequency (hourly) markets using algorithms on the basis of Lunde and Timmermann (2004) and Bry and Boschan (1971). Results from Section 4 showed that hourly returns of Ethereum, Bitcoin, and Litecoin during a bull market exhibited a random walk (market efficiency) when using a rolling DFA Hurst exponent test. However, when conditions changed and the market entered a bear-market period, we saw signs that the market started to show persistence positive autocorrelation behaviour (market inefficiency).

In addition, we utilised six different tests to investigate market efficiency using a nonrolling fixed period. During the bull- and bear-market periods, the hourly returns of the three cryptocurrencies exhibited market inefficiency.

Similar results could be seen for other financial markets, for example, Gil-Alana et al. (2018) noted that the Baltic stock market rejected the theory of market efficiency during bull- and bear-market states; Jiang and Li (2019) investigated market efficiency for the Chinese, Japanese, and U.S. stock markets, and found market inefficiency in bull- and bear-market states. Furthermore, the Amihud illiquidity ratio illustrated that, in a bear market, hourly Bitcoin returns become more liquid. In contrast, hourly Ethereum and Litecoin returns exhibit less liquidity in this period compared to during a bull-market period.

In addition, we saw that volatility of hourly returns of all three cryptocurrencies decreased during a bear market. There is much scope for future work, and possible extensions could include: (i) focusing not only on hourly, but also higher-frequency data (minutes) due to movement towards higher-frequency cryptocurrency trading; (ii) further investigations into how these results for bull and bear markets could be used for arbitrage or trading strategies, for example, if there is inefficiency in the market during particular periods, if we could use market properties to monitor and predict *J. Risk Financial Manag.* **2020**, *13*, 8

when it would be the best time to buy or sell; (iii) investigate how to define bull and bear periods in a high-frequency market. Theoretically, there are many short bull- and bear-market periods within our two subsamples, so this may be more useful if we are considering trading at a higher-frequency level.

**Author Contributions:** Conceptualization, Y.Z.; Methodology, H.S., S.C., J.C. and Y.Z.; Software, Y.Z., and J.C,.; Validation Y.Z.; Formal Analysis, H.S., S.C., J.C. and Y.Z.; Investigation, H.S., S.C., J.C. and Y.Z.; Resources, H.S., S.C., J.C. and Y.Z.; Data Curation, H.S., and Y.Z.; Writing—Original Draft Preparation, H.S., S.C., J.C. and Y.Z.; Writing—Review & Editing, H.S., S.C., J.C. and Y.Z.; Visualization, H.S., S.C., J.C. and Y.Z.; Supervision, S.C., and J.C.; Project Administration, Y.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
