Causal relationships between cryptocurrencies: the effects of sampling interval and sample size

Nezir Köse; Emre Ünal

doi:10.1515/snde-2022-0054

Abstract

For this paper, the relationship between seventeen popular cryptocurrencies was analyzed by multivariate Granger causality tests and simple linear regression, using data spanning the period 1 September 2020 to 8 December 2021. The novelty of this work is that it studies the effects of sampling interval and sample size in cryptocurrency markets, which can yield significantly different results. Minute-by-minute, hourly and daily data were collected to examine the Granger causality relationship between cryptocurrencies. It was found that all the currencies demonstrated a significant causality relationship when high frequency (such as minute-by-minute) data was used, in contrast to hourly and daily data. The bigger the sample size, the higher the probability of rejecting the null hypothesis. Hence, the null hypothesis for the Granger causality test can be rejected for minute-by-minute time series data because of too large a sample size. Granger causality test results for hourly and daily data indicated that Bitcoin, Ethereum Classic, and Neo were leading indicators among the cryptocurrencies included in the research. In addition, according to simple linear regression analysis, the short term marginal effect of Bitcoin plays an important role by creating significant impacts on other cryptocurrencies.

Keywords: cryptocurrency; multivariate Granger causality test; sample size; sampling interval; simple linear regression

JEL Classification: C5; F3; G1

Corresponding author: Emre Ünal, Department of Economics, Firat University, Merkez, 23119, Elazig, Türkiye, E-mail: eunal@firat.edu.tr

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: Not applicable.
Conflict of interest statement: The authors declare that they have no conflict of interest.
Availability of data and materials: Various sources were used to collect data for the analyses. Each source of data and materials has been available and pointed through the paper.
Consent for publication: Not applicable.
Ethics approval and consent to participate: This article does not contain any studies with human participants performed by any of the authors.

Appendix A

Table 1A:

Multivariate Granger causality test results.

Dependent variable is Bnb							Dependent variable is Btc
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Btc	381.0	0.000^*	34.4	0.001^*	0.6	0.4331	Bnb	17,356.8	0.000^*	17.4	0.180	0.1	0.7959
Btt	334.4	0.000^*	41.9	0.000^*	1.9	0.1685	Btt	478.0	0.000^*	24.8	0.024^**	0.2	0.6559
Cel	363.0	0.000^*	25.6	0.019^**	0.0	0.9715	Cel	603.5	0.000^*	10.7	0.633	0.6	0.4306
Dash	317.2	0.000^*	14.7	0.328	0.3	0.5831	Dash	3243.9	0.000^*	12.3	0.503	0.1	0.7718
Eos	445.5	0.000^*	19.2	0.117	0.3	0.6085	Eos	4876.8	0.000^*	11.1	0.604	1.9	0.1730
Etc	322.9	0.000^*	23.9	0.032^**	0.0	0.8604	Etc	4655.0	0.000^*	21.0	0.073	0.0	0.9801
Eth	415.1	0.000^*	24.5	0.027^**	1.1	0.2851	Eth	16,388.1	0.000^*	25.4	0.021^**	0.4	0.5494
Link	296.2	0.000^*	23.2	0.040^**	1.9	0.1668	Link	5620.2	0.000^*	29.6	0.006^*	0.8	0.3658
Ltc	465.4	0.000^*	9.1	0.766	0.0	0.8660	Ltc	1906.5	0.000^*	12.7	0.474	1.6	0.2122
Neo	420.7	0.000^*	22.0	0.055	0.6	0.4347	Neo	2087.8	0.000^*	16.7	0.214	3.0	0.0825
One	164.7	0.000^*	32.3	0.002^*	2.2	0.1367	One	508.9	0.000^*	20.7	0.080	0.9	0.3556
Qtum	886.0	0.000^*	12.7	0.474	0.1	0.8140	Qtum	1736.9	0.000^*	7.2	0.893	0.5	0.4779
Trx	196.4	0.000^*	37.0	0.000^*	0.3	0.5677	Trx	2175.2	0.000^*	14.9	0.317	0.4	0.5497
Xlm	286.2	0.000^*	11.2	0.596	0.2	0.6783	Xlm	1769.6	0.000^*	29.7	0.005^*	3.8	0.0509
Xmr	434.7	0.000^*	20.9	0.075	0.2	0.6398	Xmr	249.4	0.000^*	20.1	0.094	0.5	0.4920
Zec	451.9	0.000^*	29.4	0.006^*	1.0	0.3121	Zec	3653.4	0.000^*	24.0	0.031^**	1.1	0.3013
All	8752	0.000^*	418	0.000^*	16.0	0.4501	All	747,551	0.000^*	338	0.000^*	29.4	0.0215^**

Dependent variable is Btt							Dependent variable is Cel
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	1293.7	0.000^*	21.0	0.073	0.1	0.7731	Bnb	1389.6	0.000^*	20.3	0.089	1.7	0.1859
Btc	1082.5	0.000^*	30.6	0.004^*	2.9	0.0910	Btc	610.5	0.000^*	29.5	0.006^*	1.7	0.1978
Cel	164.4	0.000^*	40.7	0.000^*	1.4	0.2426	Btt	456.9	0.000^*	38.8	0.000^*	7.2	0.0072^*
Dash	766.2	0.000^*	12.8	0.460	1.0	0.3177	Dash	697.6	0.000^*	8.5	0.809	0.1	0.7401
Eos	372.0	0.000^*	39.7	0.000^*	0.0	0.8916	Eos	681.0	0.000^*	31.4	0.003^*	1.4	0.2437
Etc	1462.7	0.000^*	26.4	0.015^**	0.8	0.3684	Etc	887.9	0.000^*	20.0	0.096	0.7	0.3953
Eth	2991.9	0.000^*	16.1	0.243	0.0	0.9106	Eth	2511.4	0.000^*	14.5	0.340	0.0	0.9649
Link	2198.2	0.000^*	29.3	0.006^*	0.8	0.3608	Link	2465.0	0.000^*	51.1	0.000^*	0.0	0.9792
Ltc	1465.8	0.000^*	18.1	0.154	0.2	0.6370	Ltc	1023.5	0.000^*	20.0	0.095	0.8	0.3598
Neo	507.2	0.000^*	18.2	0.149	2.8	0.0950	Neo	621.5	0.000^*	28.1	0.009^*	5.5	0.0188^**
One	326.6	0.000^*	21.0	0.074	0.5	0.4654	One	1330.4	0.000^*	56.6	0.000^*	0.3	0.5886
Qtum	713.1	0.000^*	24.3	0.029^**	0.5	0.4667	Qtum	871.8	0.000^*	11.5	0.573	0.1	0.7644
Trx	7271.0	0.000^*	13.3	0.427	0.2	0.6861	Trx	839.9	0.000^*	27.0	0.012^**	0.1	0.8068
Xlm	722.5	0.000^*	13.7	0.399	0.0	0.9552	Xlm	355.4	0.000^*	10.8	0.628	1.7	0.1948
Xmr	628.3	0.000^*	10.5	0.651	1.7	0.1873	Xmr	364.6	0.000^*	9.2	0.760	0.4	0.5428
Zec	307.9	0.000^*	26.8	0.013^**	0.1	0.8000	Zec	488.9	0.000^*	30.6	0.004^*	0.5	0.4784
All	68,725	0.000^*	423	0.000^*	21.0	0.1773	All	63,999	0.000^*	450	0.000^*	24.0	0.0897

Dependent variable is Dash							Dependent variable is Eos
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	293.5	0.000^*	23.5	0.036^**	9.9	0.627	Bnb	353.4	0.000^*	26.5	0.014^**	0.0	0.8882
Btc	377.5	0.000^*	25.6	0.019^**	23.2	0.027^**	Btc	474.6	0.000^*	30.8	0.004^*	3.7	0.0545
Btt	185.7	0.000^*	8.6	0.803	14.9	0.246	Btt	319.0	0.000^*	19.7	0.103	0.2	0.6905
Cel	218.0	0.000^*	14.0	0.376	15.5	0.214	Cel	245.1	0.000^*	18.2	0.148	2.1	0.1440
Eos	359.1	0.000^*	6.2	0.940	25.1	0.014^**	Dash	202.4	0.000^*	22.8	0.044^**	1.6	0.2102
Etc	430.0	0.000^*	37.8	0.000^*	14.4	0.274	Etc	632.0	0.000^*	42.4	0.000^*	5.1	0.0237^**
Eth	463.9	0.000^*	12.8	0.465	11.0	0.526	Eth	379.2	0.000^*	9.3	0.751	0.1	0.6994
Link	279.2	0.000^*	32.6	0.002^*	13.0	0.368	Link	531.6	0.000^*	36.3	0.001^*	0.7	0.3977
Ltc	721.5	0.000^*	14.9	0.313	15.4	0.219	Ltc	1146.1	0.000^*	23.1	0.041^**	1.0	0.3121
Neo	279.1	0.000^*	11.3	0.585	24.2	0.019^**	Neo	408.6	0.000^*	13.5	0.408	6.7	0.0098^*
One	169.0	0.000^*	28.9	0.007^*	8.9	0.711	One	160.1	0.000^*	34.7	0.001^*	0.0	0.9330
Qtum	1023.7	0.000^*	10.2	0.680	11.5	0.486	Qtum	1344.6	0.000^*	19.8	0.100	0.8	0.3582
Trx	178.6	0.000^*	11.9	0.538	7.5	0.825	Trx	234.3	0.000^*	32.3	0.002^*	3.6	0.0585
Xlm	256.0	0.000^*	32.0	0.002^*	14.3	0.280	Xlm	473.2	0.000^*	36.5	0.001^*	2.9	0.0875
Xmr	380.5	0.000^*	15.6	0.271	7.6	0.814	Xmr	399.4	0.000^*	24.2	0.029^**	1.1	0.3035
Zec	523.2	0.000^*	41.5	0.000^*	11.2	0.512	Zec	592.0	0.000^*	32.0	0.002^*	0.1	0.8220
All	8037	0.000^*	370.8	0.000^*	263.8	0.001^*	All	10,471	0.000^*	454	0.000^*	32.9	0.0077^*

Dependent variable is Etc							Dependent variable is Eth
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	352.8	0.000^*	17.6	0.172	0.2	0.6796	Bnb	2537.0	0.000^*	15.1	0.299	0.2	0.6538
Btc	423.6	0.000^*	25.7	0.018^**	0.0	0.8721	Btc	560.8	0.000^*	37.0	0.000^*	6.0	0.0146^**
Btt	321.0	0.000^*	10.8	0.624	0.7	0.4092	Btt	1294.0	0.000^*	8.2	0.833	0.2	0.6674
Cel	296.7	0.000^*	23.9	0.033^**	2.8	0.0932	Cel	274.7	0.000^*	10.5	0.649	2.9	0.0900
Dash	319.1	0.000^*	22.3	0.050^***	3.3	0.0688	Dash	1085.6	0.000^*	11.0	0.611	0.9	0.3391
Eos	708.8	0.000^*	16.2	0.239	5.2	0.0230**	Eos	1085.4	0.000^*	16.6	0.218	0.7	0.3887
Eth	631.8	0.000^*	22.9	0.043^**	0.0	0.8976	Etc	2564.6	0.000^*	18.5	0.139	0.1	0.7087
Link	326.4	0.000^*	25.9	0.018^**	0.0	0.9763	Link	7385.1	0.000^*	32.5	0.002^*	0.1	0.7569
Ltc	763.5	0.000^*	19.0	0.125	5.0	0.0250**	Ltc	1742.5	0.000^*	18.2	0.151	1.1	0.2851
Neo	370.8	0.000^*	23.3	0.038^**	8.0	0.0047^*	Neo	747.4	0.000^*	24.2	0.029^**	4.7	0.0299^**
One	227.2	0.000^*	29.8	0.005^*	0.4	0.5378	One	491.1	0.000^*	29.4	0.006	0.0	0.9676
Qtum	1025.1	0.000^*	23.7	0.034^**	0.6	0.4220	Qtum	1396.9	0.000^*	7.6	0.871	1.0	0.3144
Trx	389.6	0.000^*	36.9	0.000^*	0.4	0.5381	Trx	1019.1	0.000^*	13.9	0.382	0.3	0.6046
Xlm	352.3	0.000^*	14.2	0.361	0.8	0.3627	Xlm	1208.1	0.000^*	19.2	0.118	1.0	0.3220
Xmr	452.8	0.000^*	11.6	0.559	2.5	0.1155	Xmr	865.3	0.000^*	11.1	0.598	0.1	0.8093
Zec	454.3	0.000^*	60.7	0.000^*	0.1	0.7928	Zec	1239.6	0.000^*	31.3	0.003*	1.1	0.2968
All	9441	0.000^*	416	0.000^*	36.8	0.0022*	All	100,348	0.000^*	342.0	0.000^*	31.8	0.0106^**

Dependent variable is Link							Dependent variable is Ltc
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	219.2	0.000^*	12.8	0.465	0.0	0.9603	Bnb	2617.1	0.000^*	9.5	0.734	0.1	0.7654
Btc	394.2	0.000^*	37.3	0.000^*	3.9	0.0495^**	Btc	498.6	0.000^*	35.8	0.001^*	8.8	0.0031^*
Btt	212.7	0.000^*	11.8	0.541	0.2	0.6523	Btt	413.7	0.000^*	15.4	0.281	0.2	0.6965
Cel	253.9	0.000^*	14.1	0.368	2.6	0.1036	Cel	516.1	0.000^*	22.0	0.056	6.0	0.0145^**
Dash	281.3	0.000^*	18.2	0.150	0.5	0.4714	Dash	2960.5	0.000^*	15.1	0.301	0.2	0.6686
Eos	362.6	0.000^*	8.3	0.826	0.7	0.4199	Eos	5939.7	0.000^*	17.3	0.187	2.1	0.1456
Etc	335.4	0.000^*	18.3	0.146	3.9	0.0497^**	Etc	4294.3	0.000^*	17.6	0.174	1.7	0.1895
Eth	379.3	0.000^*	13.2	0.436	0.4	0.5162	Eth	609.6	0.000^*	17.9	0.163	0.0	0.8589
Ltc	487.8	0.000^*	13.3	0.428	0.5	0.4638	Link	5791.4	0.000^*	24.6	0.026^**	0.0	0.8284
Neo	322.5	0.000^*	23.3	0.039^**	5.5	0.0186^**	Neo	1045.3	0.000^*	31.6	0.003^*	4.2	0.0406^**
One	202.1	0.000^*	38.1	0.000^*	0.0	0.8744	One	463.8	0.000^*	28.0	0.009^*	0.0	0.9179
Qtum	1011.8	0.000^*	17.3	0.186	0.1	0.7514	Qtum	1563.4	0.000^*	8.2	0.830	0.0	0.8373
Trx	290.3	0.000^*	16.7	0.212	0.0	0.9226	Trx	778.2	0.000^*	8.0	0.841	2.0	0.1612
Xlm	226.9	0.000^*	11.4	0.578	0.4	0.5037	Xlm	4491.9	0.000^*	13.2	0.433	0.9	0.3557
Xmr	310.7	0.000^*	15.1	0.300	0.2	0.6291	Xmr	1853.0	0.000^*	21.1	0.070	2.4	0.1187
Zec	438.8	0.000^*	32.0	0.002^*	0.4	0.5282	Zec	2032.0	0.000^*	23.3	0.038^**	1.0	0.3139
All	8314	0.000^*	344	0.000^*	23.2	0.1087	All	235,899	0.000^*	388	0.000^*	40.2	0.0007^*

Dependent variable is Neo							Dependent variable is One
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	275.0	0.000^*	24.4	0.028^**	0.4	0.5229	Bnb	2118.3	0.000^*	24.3	0.028^**	0.6	0.4240
Btc	554.5	0.000^*	33.7	0.001^*	2.2	0.1408	Btc	987.2	0.000^*	17.7	0.171	2.2	0.1404
Btt	302.0	0.000^*	14.0	0.372	4.8	0.0291^**	Btt	534.7	0.000^*	39.6	0.000^*	9.6	0.0020^*
Cel	187.2	0.000^*	23.0	0.041^**	0.1	0.7479	Cel	448.0	0.000^*	28.6	0.007^*	1.3	0.2457
Dash	349.3	0.000^*	7.0	0.903	0.1	0.7211	Dash	1032.5	0.000^*	17.2	0.188	0.3	0.5632
Eos	416.5	0.000^*	23.2	0.040^**	7.9	0.0048^*	Eos	867.7	0.000^*	25.6	0.020^**	1.5	0.2136
Etc	666.1	0.000^*	29.7	0.005^*	11.7	0.0006^*	Etc	1549.4	0.000^*	23.5	0.036^**	3.1	0.0800
Eth	496.1	0.000^*	10.2	0.679	0.3	0.5684	Eth	2563.5	0.000^*	16.8	0.206	0.2	0.6897
Link	417.3	0.000^*	47.5	0.000^*	0.1	0.7408	Link	3034.2	0.000^*	35.6	0.001^*	0.7	0.4164
Ltc	710.8	0.000^*	30.5	0.004^*	0.0	0.8871	Ltc	2059.1	0.000^*	19.5	0.107	0.4	0.5069
One	175.3	0.000^*	22.4	0.049^**	0.9	0.3477	Neo	939.4	0.000^*	17.5	0.179	1.9	0.1733
Qtum	2355.7	0.000^*	9.5	0.738	0.0	0.9678	Qtum	823.4	0.000^*	15.7	0.265	0.0	0.9898
Trx	267.4	0.000^*	31.0	0.003^*	0.0	0.9024	Trx	1038.6	0.000^*	6.8	0.910	1.3	0.2494
Xlm	517.2	0.000^*	9.5	0.735	2.3	0.1284	Xlm	544.7	0.000^*	10.3	0.668	2.5	0.1173
Xmr	454.5	0.000^*	15.0	0.306	0.5	0.4800	Xmr	681.7	0.000^*	8.9	0.777	0.3	0.5915
Zec	528.7	0.000^*	68.5	0.000^*	1.0	0.3231	Zec	481.4	0.000^*	29.6	0.005^*	0.8	0.3742
All	12,221	0.000^*	441	0.000^*	28.4	0.0285^**	All	73,582	0.000^*	360	0.000^*	26.2	0.0512

Dependent variable is Qtum							Dependent variable is Trx
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	251.8	0.000^*	30.5	0.004^*	0.1	0.7320	Bnb	230.8	0.000^*	17.6	0.174	2.7	0.1012
Btc	357.4	0.000^*	26.2	0.016^**	1.8	0.1848	Btc	374.3	0.000^*	43.9	0.000^*	0.8	0.3848
Btt	162.6	0.000^*	21.8	0.059	1.1	0.3050	Btt	1074.4	0.000^*	45.7	0.000^*	4.2	0.0402^**
Cel	179.6	0.000^*	12.1	0.520	1.4	0.2359	Cel	227.7	0.000^*	20.3	0.088	0.5	0.4998
Dash	259.9	0.000^*	7.9	0.850	4.6	0.0316^**	Dash	251.8	0.000^*	15.0	0.305	0.7	0.3982
Eos	532.0	0.000^*	20.0	0.095	1.0	0.3062	Eos	488.1	0.000^*	26.2	0.016^**	4.3	0.0374^**
Etc	640.3	0.000^*	44.0	0.000^*	9.6	0.0019^*	Etc	503.9	0.000^*	31.2	0.003^*	1.0	0.3130
Eth	322.0	0.000^*	8.3	0.825	0.2	0.6186	Eth	283.8	0.000^*	24.9	0.024^**	0.0	0.8928
Link	266.2	0.000^*	32.7	0.002^*	0.1	0.6986	Link	259.1	0.000^*	29.7	0.005^*	0.1	0.7428
Ltc	480.2	0.000^*	22.1	0.053	0.1	0.7170	Ltc	708.6	0.000^*	16.5	0.222	0.3	0.6168
Neo	472.0	0.000^*	24.1	0.030^**	0.6	0.4454	Neo	266.2	0.000^*	23.7	0.034^**	9.5	0.0020^*
One	185.3	0.000^*	26.5	0.014^**	1.0	0.3122	One	158.6	0.000^*	20.2	0.092	0.4	0.5303
Trx	216.0	0.000^*	41.5	0.000^*	0.4	0.5504	Qtum	843.4	0.000^*	12.8	0.467	3.9	0.0484^**
Xlm	341.9	0.000^*	17.2	0.190	0.1	0.7466	Xlm	292.7	0.000^*	59.5	0.000^*	0.6	0.4531
Xmr	296.1	0.000^*	10.2	0.678	2.6	0.1089	Xmr	287.5	0.000^*	6.4	0.929	0.8	0.3762
Zec	459.3	0.000^*	54.6	0.000^*	0.2	0.6419	Zec	315.3	0.000^*	32.4	0.002^*	0.2	0.6264
All	7396	0.000^*	431	0.000^*	21.0	0.1768	All	8958	0.000^*	455	0.000^*	27.3	0.0379^**

Dependent variable is Xlm							Dependent variable is Xmr
	Minute-by-		Hourly data		Daily data			Minute-by-		Hourly data		Daily data
	minute data							minute data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.	X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	1344.5	0.000^*	25.2	0.022^**	0.2	0.6725	Bnb	3084.9	0.000^*	20.3	0.089	0.7	0.3909
Btc	301.8	0.000^*	17.2	0.192	0.4	0.5227	Btc	302.1	0.000^*	23.2	0.040^**	1.7	0.1954
Btt	128.0	0.000^*	5.2	0.971	0.2	0.6941	Btt	159.7	0.000^*	9.0	0.774	0.9	0.3490
Cel	398.4	0.000^*	15.2	0.293	0.7	0.4035	Cel	742.4	0.000^*	18.7	0.133	0.2	0.6683
Dash	1744.5	0.000^*	5.4	0.966	0.0	0.9610	Dash	4312.4	0.000^*	31.3	0.003^*	0.9	0.3466
Eos	3192.8	0.000^*	23.1	0.041^**	3.6	0.0562	Eos	3188.4	0.000^*	24.7	0.025^**	0.0	0.9366
Etc	2997.9	0.000^*	34.1	0.001^*	0.6	0.4252	Etc	2779.7	0.000^*	17.5	0.177	2.0	0.1523
Eth	585.1	0.000^*	25.4	0.020^**	2.6	0.1055	Eth	687.7	0.000^*	21.6	0.062	0.3	0.6097
Link	4327.4	0.000^*	21.0	0.073	1.8	0.1848	Link	4176.6	0.000^*	22.0	0.056	1.8	0.1836
Ltc	7863.3	0.000^*	14.6	0.333	0.0	0.8540	Ltc	10,032.9	0.000^*	26.6	0.014^**	0.4	0.5033
Neo	1488.2	0.000^*	29.6	0.005^*	2.2	0.1389	Neo	1529.9	0.000^*	19.5	0.109	0.6	0.4401
One	424.6	0.000^*	22.7	0.045^**	0.0	0.9200	One	637.7	0.000^*	33.3	0.002^*	1.8	0.1828
Qtum	1455.8	0.000^*	24.5	0.027^**	0.3	0.6159	Qtum	1906.9	0.000^*	8.7	0.798	0.4	0.5200
Trx	751.3	0.000^*	27.9	0.009^*	0.5	0.4595	Trx	595.0	0.000^*	25.1	0.023^**	0.1	0.8078
Xmr	1608.9	0.000^*	12.6	0.482	1.3	0.2579	Xlm	3971.7	0.000^*	8.8	0.788	1.1	0.2928
Zec	1411.1	0.000^*	39.4	0.000*	0.0	0.9386	Zec	4332.3	0.000^*	66.8	0.000^*	0.2	0.6485
All	162,926	0.000^*	410	0.000^*	20.6	0.1960	All	225,132	0.000^*	397	0.000^*	16.6	0.4093

Dependent variable is Zec
	Minute-by-minute data		Hourly data		Daily data
X	χ ²	Prob.	χ ²	Prob.	χ ²	Prob.
Bnb	306.8	0.000^*	25.5	0.020^**	0.1	0.7528
Btc	506.9	0.000^*	20.7	0.079	0.8	0.3654
Btt	230.2	0.000^*	12.6	0.475	0.5	0.4823
Cel	197.5	0.000^*	14.4	0.346	1.3	0.2563
Dash	1001.3	0.000^*	38.1	0.000^*	1.5	0.2205
Eos	537.5	0.000^*	24.0	0.031^**	0.0	0.9072
Etc	474.4	0.000^*	23.9	0.032^**	0.5	0.4872
Eth	585.7	0.000^*	14.8	0.320	0.0	0.9588
Link	352.5	0.000^*	22.8	0.044^**	1.2	0.2648
Ltc	715.4	0.000^*	18.6	0.136	0.5	0.4647
Neo	282.8	0.000^*	15.2	0.296	5.3	0.0213^**
One	216.3	0.000^*	24.6	0.026^**	0.0	0.8898
Qtum	941.7	0.000^*	15.2	0.294	2.8	0.0942
Trx	258.6	0.000^*	21.9	0.056	0.0	0.9377
Xlm	273.8	0.000^*	24.7	0.026^**	0.4	0.5273
Xmr	397.3	0.000^*	21.4	0.065	1.4	0.2406
All	9701.9	0.000^*	410.4	0.000^*	17.3	0.3664

^*Indicate significance at the 1% level. ^**Indicate significance at the 5% level.

Table 2A:

Results of simple linear regression in logarithmic first difference for daily data.

Dependent variable is Bnb				Dependent variable is Btc				Dependent variable is Btt
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Btc	1.06	0.0000	0.379	Bnb	0.36	0.0000	0.379	Bnb	0.63	0.0000	0.286
Btt	0.46	0.0000	0.286	Btt	0.30	0.0000	0.380	Btc	1.06	0.0000	0.380
Cel	0.33	0.0000	0.200	Cel	0.21	0.0000	0.237	Cel	0.43	0.0000	0.242
Dash	0.60	0.0000	0.374	Dash	0.37	0.0000	0.430	Dash	0.64	0.0000	0.309
Eos	0.58	0.0000	0.372	Eos	0.36	0.0000	0.437	Eos	0.67	0.0000	0.366
Etc	0.50	0.0000	0.273	Etc	0.33	0.0000	0.343	Etc	0.58	0.0000	0.260
Eth	0.82	0.0000	0.417	Eth	0.56	0.0000	0.586	Eth	0.85	0.0000	0.324
Link	0.61	0.0000	0.408	Link	0.37	0.0000	0.451	Link	0.61	0.0000	0.298
Ltc	0.70	0.0000	0.400	Ltc	0.51	0.0000	0.615	Ltc	0.74	0.0000	0.317
Neo	0.66	0.0000	0.444	Neo	0.39	0.0000	0.458	Neo	0.70	0.0000	0.369
One	0.34	0.0000	0.227	One	0.19	0.0000	0.211	One	0.39	0.0000	0.210
Qtum	0.51	0.0000	0.378	Qtum	0.29	0.0000	0.364	Qtum	0.53	0.0000	0.300
Trx	0.62	0.0000	0.323	Trx	0.39	0.0000	0.371	Trx	0.90	0.0000	0.495
Xlm	0.50	0.0000	0.281	Xlm	0.34	0.0000	0.373	Xlm	0.56	0.0000	0.249
Xmr	0.71	0.0000	0.372	Xmr	0.45	0.0000	0.445	Xmr	0.74	0.0000	0.293
Zec	0.59	0.0000	0.384	Zec	0.36	0.0000	0.428	Zec	0.62	0.0000	0.311

Dependent variable is Cel				Dependent variable is Dash				Dependent variable is Eos
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Bnb	0.61	0.0000	0.200	Bnb	0.63	0.0000	0.374	Bnb	0.65	0.0000	0.372
Btc	1.14	0.0000	0.237	Btc	1.16	0.0000	0.430	Btc	1.21	0.0000	0.437
Btt	0.57	0.0000	0.242	Btt	0.49	0.0000	0.309	Btt	0.55	0.0000	0.366
Dash	0.65	0.0000	0.240	Cel	0.37	0.0000	0.240	Cel	0.41	0.0000	0.280
Eos	0.68	0.0000	0.280	Eos	0.73	0.0000	0.571	Dash	0.78	0.0000	0.571
Etc	0.60	0.0000	0.210	Etc	0.76	0.0000	0.596	Etc	0.78	0.0000	0.593
Eth	0.97	0.0000	0.314	Eth	0.89	0.0000	0.465	Eth	0.94	0.0000	0.491
Link	0.80	0.0000	0.384	Link	0.68	0.0000	0.477	Link	0.74	0.0000	0.532
Ltc	0.84	0.0000	0.310	Ltc	0.89	0.0000	0.601	Ltc	0.92	0.0000	0.610
Neo	0.73	0.0000	0.293	Neo	0.77	0.0000	0.574	Neo	0.82	0.0000	0.609
One	0.68	0.0000	0.480	One	0.35	0.0000	0.224	One	0.36	0.0000	0.221
Qtum	0.58	0.0000	0.265	Qtum	0.57	0.0000	0.457	Qtum	0.67	0.0000	0.585
Trx	0.80	0.0000	0.292	Trx	0.75	0.0000	0.445	Trx	0.84	0.0000	0.531
Xlm	0.62	0.0000	0.233	Xlm	0.61	0.0000	0.395	Xlm	0.74	0.0000	0.537
Xmr	0.70	0.0000	0.198	Xmr	0.88	0.0000	0.550	Xmr	0.77	0.0000	0.393
Zec	0.67	0.0000	0.268	Zec	0.82	0.0000	0.708	Zec	0.72	0.0000	0.511

Dependent variable is Etc				Dependent variable is Eth				Dependent variable is Link
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Bnb	0.54	0.0000	0.273	Bnb	0.51	0.0000	0.417	Bnb	0.67	0.0000	0.408
Btc	1.05	0.0000	0.343	Btc	1.04	0.0000	0.586	Btc	1.21	0.0000	0.451
Btt	0.45	0.0000	0.260	Btt	0.38	0.0000	0.324	Btt	0.49	0.0000	0.298
Cel	0.35	0.0000	0.210	Cel	0.32	0.0000	0.314	Cel	0.48	0.0000	0.384
Dash	0.78	0.0000	0.596	Dash	0.52	0.0000	0.465	Dash	0.70	0.0000	0.477
Eos	0.76	0.0000	0.593	Eos	0.52	0.0000	0.491	Eos	0.72	0.0000	0.532
Eth	0.90	0.0000	0.463	Etc	0.51	0.0000	0.463	Etc	0.68	0.0000	0.451
Link	0.67	0.0000	0.451	Link	0.61	0.0000	0.650	Eth	1.07	0.0000	0.650
Ltc	0.86	0.0000	0.556	Ltc	0.70	0.0000	0.641	Ltc	0.90	0.0000	0.595
Neo	0.77	0.0000	0.564	Neo	0.57	0.0000	0.539	Neo	0.80	0.0000	0.590
One	0.30	0.0000	0.165	One	0.28	0.0000	0.237	One	0.41	0.0000	0.294

Dependent variable is Etc				Dependent variable is Eth				Dependent variable is Link
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Qtum	0.63	0.0000	0.528	Qtum	0.44	0.0000	0.449	Qtum	0.61	0.0000	0.496
Trx	0.74	0.0000	0.425	Trx	0.57	0.0000	0.446	Trx	0.76	0.0000	0.441
Xlm	0.62	0.0000	0.386	Xlm	0.48	0.0000	0.419	Xlm	0.67	0.0000	0.455
Xmr	0.75	0.0000	0.390	Xmr	0.59	0.0000	0.423	Xmr	0.77	0.0000	0.404
Zec	0.70	0.0000	0.501	Zec	0.53	0.0000	0.504	Zec	0.70	0.0000	0.498

Dependent variable is Ltc				Dependent variable is Neo				Dependent variable is One
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Bnb	0.57	0.0000	0.400	Bnb	0.67	0.0000	0.444	Bnb	0.66	0.0000	0.227
Btc	1.21	0.0000	0.615	Btc	1.18	0.0000	0.458	Btc	1.10	0.0000	0.211
Btt	0.43	0.0000	0.317	Btt	0.52	0.0000	0.369	Btt	0.54	0.0000	0.210
Cel	0.37	0.0000	0.310	Cel	0.40	0.0000	0.293	Cel	0.71	0.0000	0.480
Dash	0.68	0.0000	0.601	Dash	0.75	0.0000	0.574	Dash	0.64	0.0000	0.224
Eos	0.66	0.0000	0.610	Eos	0.75	0.0000	0.609	Eos	0.62	0.0000	0.221
Etc	0.64	0.0000	0.556	Etc	0.73	0.0000	0.564	Etc	0.54	0.0000	0.165
Eth	0.91	0.0000	0.641	Eth	0.94	0.0000	0.539	Eth	0.86	0.0000	0.237
Link	0.66	0.0000	0.595	Link	0.74	0.0000	0.590	Link	0.72	0.0000	0.294
Neo	0.68	0.0000	0.586	Ltc	0.86	0.0000	0.586	Ltc	0.80	0.0000	0.268
One	0.34	0.0000	0.268	One	0.38	0.0000	0.271	Neo	0.71	0.0000	0.271
Qtum	0.53	0.0000	0.517	Qtum	0.67	0.0000	0.637	Qtum	0.55	0.0000	0.230
Trx	0.65	0.0000	0.443	Trx	0.81	0.0000	0.536	Trx	0.73	0.0000	0.236
Xlm	0.57	0.0000	0.438	Xlm	0.66	0.0000	0.467	Xlm	0.56	0.0000	0.183
Xmr	0.73	0.0000	0.489	Xmr	0.81	0.0000	0.476	Xmr	0.73	0.0000	0.208
Zec	0.65	0.0000	0.579	Zec	0.72	0.0000	0.572	Zec	0.64	0.0000	0.236

Dependent variable is Qtum				Dependent variable is Trx				Dependent variable is Xlm
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Bnb	0.74	0.0000	0.378	Bnb	0.52	0.0000	0.323	Bnb	0.56	0.0000	0.281
Btc	1.26	0.0000	0.364	Btc	0.96	0.0000	0.371	Btc	1.11	0.0000	0.373
Btt	0.56	0.0000	0.300	Btt	0.55	0.0000	0.495	Btt	0.45	0.0000	0.249
Cel	0.46	0.0000	0.265	Cel	0.36	0.0000	0.292	Cel	0.37	0.0000	0.233
Dash	0.80	0.0000	0.457	Dash	0.59	0.0000	0.445	Dash	0.64	0.0000	0.395
Eos	0.87	0.0000	0.585	Eos	0.63	0.0000	0.531	Eos	0.73	0.0000	0.537
Etc	0.84	0.0000	0.528	Etc	0.57	0.0000	0.425	Etc	0.63	0.0000	0.386
Eth	1.03	0.0000	0.449	Eth	0.78	0.0000	0.446	Eth	0.86	0.0000	0.419
Link	0.81	0.0000	0.496	Link	0.58	0.0000	0.441	Link	0.68	0.0000	0.455
Ltc	0.97	0.0000	0.517	Ltc	0.68	0.0000	0.443	Ltc	0.77	0.0000	0.438
Neo	0.95	0.0000	0.637	Neo	0.66	0.0000	0.536	Neo	0.71	0.0000	0.467
One	0.42	0.0000	0.230	One	0.32	0.0000	0.236	One	0.32	0.0000	0.183
Trx	0.84	0.0000	0.408	Qtum	0.48	0.0000	0.408	Qtum	0.57	0.0000	0.437
Xlm	0.76	0.0000	0.437	Xlm	0.55	0.0000	0.403	Trx	0.73	0.0000	0.403
Xmr	0.87	0.0000	0.385	Xmr	0.63	0.0000	0.348	Xmr	0.68	0.0000	0.310
Zec	0.77	0.0000	0.450	Zec	0.58	0.0000	0.442	Zec	0.64	0.0000	0.419

Dependent variable is Xmr				Dependent variable is Zec
Variable	Coef.	p-Value	R-sq	Variable	Coef.	p-Value	R-sq
Bnb	0.53	0.0000	0.372	Bnb	0.65	0.0000	0.384
Btc	1.00	0.0000	0.445	Btc	1.19	0.0000	0.428
Btt	0.40	0.0000	0.293	Btt	0.50	0.0000	0.311
Cel	0.28	0.0000	0.198	Cel	0.40	0.0000	0.268
Dash	0.62	0.0000	0.550	Dash	0.87	0.0000	0.708
Eos	0.51	0.0000	0.393	Eos	0.71	0.0000	0.511
Etc	0.52	0.0000	0.390	Etc	0.72	0.0000	0.501
Eth	0.71	0.0000	0.423	Eth	0.95	0.0000	0.504
Link	0.52	0.0000	0.404	Link	0.71	0.0000	0.498
Ltc	0.67	0.0000	0.489	Ltc	0.89	0.0000	0.579
Neo	0.59	0.0000	0.476	Neo	0.79	0.0000	0.572
One	0.28	0.0000	0.208	One	0.37	0.0000	0.236
Qtum	0.44	0.0000	0.385	Qtum	0.59	0.0000	0.450
Trx	0.56	0.0000	0.348	Trx	0.77	0.0000	0.442
Xlm	0.46	0.0000	0.310	Xlm	0.65	0.0000	0.419
Zec	0.63	0.0000	0.600	Xmr	0.95	0.0000	0.600

Standard errors are corrected for autocorrelation and/or heteroscedasticity with the Newey–West HAC. The bold values indicate the explanatory power.

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/snde-2022-0054).

Received: 2022-06-28

Revised: 2023-01-23

Accepted: 2023-02-07

Published Online: 2023-02-27

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Supplementary Material Details

Causal relationships between cryptocurrencies: the effects of sampling interval and sample size

Abstract

References

Supplementary Material

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