**3. Data**

In this paper, the datasets that we used consisted of historical high-frequency (hourly) prices of cryptocurrencies versus the US Dollar (USD) from 11:00 on 11 July 2017 to 00:00 on 19 September 2018 inclusive. The data were obtained from CryptoCompare (2018), and our analysis was limited to data that were available for download at the time. We chose cryptocurrencies for our analysis on the basis of the most popular cryptocurrencies traded on the GDAX exchange during that time, namely, Bitcoin, Ethereum, and Litecoin. These three cryptocurrencies accounted for around 80% of total market capitalisation for cryptocurrencies during that period, and we could therefore assume that the used datasets provide an adequate representation of the market. Chan et al. (2017) provides more details on the individual cryptocurrencies.

Before analysis, our preliminary approach in determining the bull and bear run period was to first identify the highest point (peak) in the dataset, which occurred on 16 January 2018. We then classified all data points prior to the peak (from 1 July 2017 to 16 January 2018) as being part of a general bull run in the market, and all points after the peak (17 January 2018 to 19 September 2018) as part of a general bear market run. However, to theoretically justify our selected periods, we implemented the Bry and Boschan (1971) and Lunde and Timmermann (2004) algorithms using the parameter values mentioned in Section 2 for detecting bull and bear periods.

There are numerous software packages that could be implemented to detect bull and bear markets in financial data, and in this analysis we use the R statistical software package (2019). To implement the 'dating' and 'filtering' algorithm methods introduced by Bry and Boschan (1971), and Lunde and Timmermann (2004), respectively, in R, we used R package bbdetection. The parameter values for the two methods were set using the two commands setpar\_dating\_alg and setpar\_filtering\_alg, respectively. For the dating algorithm, we selected parameter values of

$$
\tau\_{window} = 168,\\
\tau\_{censor} = 24,\\
\tau\_{phase} = 12,\\
\tau\_{cycle} = 12,\\
\theta = 20.
$$

For the filtering algorithm, we selected parameters of

$$\lambda\_1 = 20, \lambda\_2 = 20$$

Our reasoning for the values of *λ*1, *λ*2, and *θ* was to have a consistent threshold relating to price changes in both methods to detect peaks and troughs to determine the start and end of bull- and bear-market states. In the dating algorithm, *τwindow* was selected so that, at each time point, only turning points in the one week before and after were considered. The remainder of the parameter values were chosen to remove bull- and bear-market states that were only short-lived and insignificant.

Figure 1 plots the results of these algorithms in detecting bull and bear periods in cryptocurrency data. The shaded-white (grey) areas identify periods of a bull (bear) market run in the cryptocurrency data. The top-left (-right) diagram in Figure 1 shows the result through implementing the dating (filtering) algorithm, respectively, for Ethereum. The majority of the area before the peak for both approaches has a greater proportion of shaded-white areas than grey, which indicates that, in general, the market was a bull market. In contrast, the period after the peak sees a greater proportion of shaded-grey areas, which suggests that the market was more of a bear market in that period. Similar results were also seen for Bitcoin and Litecoin using the dating and filtering algorithms. Hence, the results used in this analysis support our preliminary results. This provides us with a reasonable case for selecting our chosen time periods for the bull and bear periods in our main analysis.

3.5

Hour

**Figure 1.** Plots indicating bull–bear periods using Ethereum (**top left**) dating and (**top right**) filtering algorithm, Bitcoin (**middle left**) dating and (**middle right**) filtering algorithm, and Litecoin (**bottom left**) dating and (**bottom right**) filtering algorithm. Bull and bear periods indicated by white and grey shaded areas, respectively.

3.5

Hour

Tables 1 and 2 provide summary statistics of log returns of high-frequency (hourly) market prices during a bull and bear market. In Table 1, the summary statistics of the log returns of the market-price index for Ethereum, Bitcoin, and Litecoin versus USD in a bull market are given. The BTC/USD index had the highest minimum, first quartile, median, and mean, while it had the lowest third quartile, maximum, and range. In contrast, the LTC/USD index had the lowest minimum, first quartile, and median, while it had the highest mean, third quartile, maximum, and range. Bitcoin was the only negatively skewed cryptocurrency. All cryptocurrencies showed significantly greater peakedness than normal distribution, and the LTC/USD index gave the highest kurtosis value. In terms of index spread, the values of standard deviation and variance for all cryptocurrencies were fairly similar (almost 0).


**Table 1.** Summary statistics of log returns of hourly market price index during a bull market in ETH/USD, BTC/USD and LTC/USD.



Table 2 presents summary statistics of log returns of market price index for Ethereum, Bitcoin, and Litecoin versus USD during a bear market. Similar to Table 1, the BTC/USD index had the highest minimum, first quartile, median, and mean, while it had the lowest third quartile, maximum, and range. Litecoin had the lowest minimum, first quartile, and median, and the highest maximum and range. Once again, all cryptocurrencies showed significantly greater peakedness than normal distribution, and the LTC/USD index gave the highest kurtosis value. Compared with bull-market summary statistics, all cryptocurrencies were positively skewed, and Litecoin had the largest skewness value. With regard to variation, ETH/USD gave the greatest standard deviation and variance. Standard deviation and variance values of log returns for all cryptocurrencies were very small and close to 0.

By comparing Tables 1 and 2, there was significant difference in some statistical properties between bull and bear markets. Compared with the bull market, the values of the minimum, skewness, and kurtosis for all cryptocurrencies increased during the bear market. However, the coefficient of variation for all cryptocurrencies significantly decreased, changing from positive to negative values. The interquartile range (IQR) for all cryptocurrencies also decreased in the bear market, implying that the middle 50% of data during the bear market were less spread out.
