Forecasting and trading cryptocurrencies with machine learning under changing market conditions

Financial Innovation

Table 3 Summary statistics on the returns of bitcoin, ethereum and litecoin

	1st Sub-sample (training) 15-Aug-2015 to 23-May-2017 (648 obs.)	2nd Sub-sample (validation) 24-May-2017 to 12-Apr-2018 (324 obs.)	3rd sub-sample (test) 13-Apr-2018 to 03-Mar-2019 (325 obs.)	Overall sample 15-Aug-2015 to 03-Mar-2019 (1297 obs.)
Bitcoin
Mean (%)	0.3345***	0.3777	− 0.2210	0.2061*
Median (%)	0.2676	0.6255	0.0850	0.2294
Min. (%)	− 20.06	− 20.75	− 14.36	− 20.75
Max. (%)	11.29	22.51	10.82	22.51
SD (%)	3.111	5.700	3.271	3.958
Skewness	− 1.149	0.0571	− 0.4784	− 0.2615
Exc. kurtosis	7.807	1.743	2.635	4.807
ρ(1)	0.0004	0.0224	− 0.0752	0.0041
Ethereum
Mean (%)	0.7098**	0.3076	− 0.4048	0.3300
Median (%)	− 0.1469	0.0737	− 0.2401	− 0.1237
Min. (%)	− 31.55	− 25.89	− 20.69	− 31.55
Max. (%)	30.28	23.47	16.61	30.28
SD (%)	7.164	6.686	5.142	6.602
Skewness	0.2979	0.0443	− 0.3636	0.2066
Exc. kurtosis	3.697	1.662	2.034	3.401
ρ(1)	0.0688*	0.0263	− 0.0681	0.0418
Litecoin
Mean (%)	0.3202	0.4300	− 0.3025	0.1916
Median (%)	0.0000	− 0.0109	− 0.3210	0.0000
Min. (%)	− 20.92	− 39.52	− 14.72	− 39.52
Max. (%)	51.04	38.93	26.87	51.04
SD (%)	4.659	8.052	4.872	5.746
Skewness	2.965	0.5794	0.2720	1.264
Exc. kurtosis	28.72	4.880	3.263	12.34
ρ(1)	0.0184	0.0297	− 0.0719	0.0131

This table shows some descriptive statistics of the log-returns of bitcoin, ethereum and litecoin. The values for the first five statistics are presented in percentage. The significance of the mean return is assessed using the t-statistic with Newey–West HAC standard error, with a Bartlett kernel bandwidth of 8. ρ(1) is the first order autocorrelation. Significance at the 10%, 5% and 1% levels are denoted by *, ** and ***, respectively