**3. Data**

The data collected for the sample span from 8 August 2015 to 28 February 2019, giving a total of 1301 observations. The data can be seen in Figure 1, which shows a big spike around the end of 2017. Chinn'a "Big Three" exchanges were pending closure around that time; however, the cryptocurrencies were largely buoyed by a bullish sentiment and went up. In December 2017, the peaks were reached and a couple days later they dropped. At this time, cryptocurrencies are mainly considered as an alternative investment, due to the fact that their use for paymen<sup>t</sup> is still limited. This can create correlations with other assets in the financial market for at least two main reasons. The first regards investors, who usually allocate wealth in a global portfolio and hedge across investments; the second relates to market sentiments that spread fast among different assets. See the work of Bianchi (2018) for similar arguments.

**Figure 1.** Price of the four cryptocurrencies from 8 August 2015 to 28 February 2019.

In this paper, we consider different cryptopredictors, as described below. The choice of these cryptopredictors is due to the fact that possible correlations between cryptocurrencies and these assets can be created, because Bitcoin and other currencies are considered as an alternative investment and their use as paymen<sup>t</sup> is still poor. We use the following list of predictors for cryptocurrencies as stated in Catania et al. (2019) as proxying market sentiments: international stock index prices (the S&P 500, Nikkei 225 and Stoxx Europe 600); commodity prices (gold and silver); interest rates (the 1-month and 10-year US Treasury rates); and the VIX closing price. To study the possible dependence between cryptocurrencies, a transformation is necessary. The percentage daily log returns of cryptocurrencies is computed as follows:

$$y\_t = 100 \times \log(S\_t / S\_{t-1}),$$

where *St* is the price on day *t* and *yt* is the cryptocurrency log return. Table 1 reports the descriptive statistics of the cryptocurrencies. In Figure 2, the transformed data are plotted against time; as documented in Chu et al. (2015), the cryptocurrencies display high volatility, non-zero skewness, very high kurtosis and several spikes.


**Table 1.** Descriptive statistics, calculated between 8 August 2015 and 28 February 2019.

Ripple has the highest volatility due to the highest kurtosis. Litecoin has also a high volatility but not that high compared to Ripple. The other two (Bitcoin and Ethereum) are compared to the aforementioned cryptocurrencies less volatile, however the kurtosis is still far away from the normal distribution, which has a kurtosis of three. Another interesting statistic is the skewness; Bitcoin is the only one with a negative skewness. This indicates that the tail is at the left side of the distribution, so the probability of lower values than the mean is higher than the normal distribution, which has a skewness of zero. With a positive skewness, this is the case for the other cryptocurrencies, the opposite is true. As before, Ripple has the highest skewness, which indicates that Ripple has the highest probabilities of higher values than its mean.

In Figure 2, the transformation of daily log returns is shown. This gives some more insight into the cryptocurrencies. Ripple is the most volatile crypto, the descriptive statistics of which are also indicated. In addition, Ethereum stands out in the first half and after that it is more stable, which means that it is less volatile. Bitcoin is the most stable crypto according to Figure 2.

**Figure 2.** Daily log returns of the four cryptocurrencies.

The crypto market is open 24/7, however the predictor variables are not. For this reason, the data have to be adapted to use for forecasting. The procedure is simple; when the market is closed, for a variable, the previous value of that variable is used. This gives a return of zero, however this is the best way since the variable is actually not changing for a day. Figure 3 shows the plots of the predictor variables.

**Figure 3.** Daily log returns of the eight cryptopredictors from 8 August 2015 to 28 February 2019.
