Do cryptocurrencies and crude oil influence each other? Evidence from wavelet-based quantile-in-quantile approach

Figures & data

Table 1. Summary statistics of cryptocurrencies and crude oil returns

Statistics	BTC	BTC.D1	BTC.D4	BTC.D6	ETH	ETH.D1	ETH.D4	ETH.D6
Observ.	877	877	877	877	877	877	877	877
Mean	0.0021	0	0	0	0.003	0	0	0
Std. Dev.	0.042	0.0291	0.0104	0.0051	0.072	0.048	0.0173	0.0111
Skewness	−0.2386	−0.1611	0.2303	0.0228	0.622	−0.0225	0.4484	0.0787
Kurtosis	4.8188	4.0184	1.424	0.8112	4.013	2.0671	1.3257	0.2202
Normtest.W	0.9118	0.9362	0.9795	0.9807	0.933	0.9659	0.9809	0.988
Normtest.p	0	0	0	0	0	0	0	0
Statistics	LTC	LTC.D1	LTC.D4	LTC.D6	XMR	XMR.D1	XMR.D4	XMR.D6
Observ.	877	877	877	877	877	877	877	877
Mean	0.0006	0	0	0	0.0014	0	0	0
Std. Dev.	0.0619	0.0418	0.016	0.0079	0.0709	0.0517	0.0151	0.0094
Skewness	1.2638	0.2161	0.6704	0.6036	0.6324	0.174	0.2473	−0.0524
Kurtosis	12.322	21.745	3.5507	1.4248	5.0718	2.836	0.2586	0.0847
Normtest.W	0.8407	0.9105	0.934	0.9554	0.9355	0.9679	0.9943	0.99
Normtest.p	0	0	0	0	0	0	0	0
Statistics	XRP	XRP.D1	XRP.D4	XRP.D6	XLM	XLM.D1	XLM.D4	XLM.D6
Observ.	877	877	877	877	877	877	877	877
Mean	0.0026	0	0	0	0.0053	0	0	0
Std. Dev.	0.0666	0.0485	0.0155	0.0091	0.094	0.0663	0.0193	0.0144
Skewness	4.5593	−0.2875	0.6259	−0.7791	2.1125	0.6004	0.5311	0.3434
Kurtosis	77.2562	102.802	8.889	3.0518	17.8319	8.5355	2.6301	1.1458
Normtest.W	0.5919	0.5474	0.8626	0.9308	0.8567	0.9174	0.9691	0.9762
Normtest.p	0	0	0	0	0	0	0	0
Statistics	DASH	DASH.D1	DASH.D4	DASH.D6	OIL	OIL.D1	OIL.D4	OIL.D6
Observ.	877	877	877	877	877	877	877	877
Mean	0.0021	0	0	0	0.0003	0	0	0
Std. Dev.	0.0588	0.0418	0.0138	0.0069	0.0219	0.0163	0.0054	0.0027
Skewness	0.3105	0.2444	0.3464	0.4308	0.0778	−0.103	0.1336	−0.283
Kurtosis	3.4902	2.3709	1.339	0.2888	2.3307	1.9324	1.5837	0.1506
Normtest.W	0.9446	0.9651	0.9807	0.9798	0.9708	0.9791	0.9839	0.9863
Normtest.p	0	0	0	0	0	0	0	0

Note: Normtest.W indicate Shapiro-Wilk test of normality which is rejected at all conventional level of significance. D1, D4, D6 denotes short-, medium- and long-term, respectively. BTC, Bitcoin; ETH, Ethereum; LTC, Litecoin; XRP, Ripple; XMR, Monero; XLM, Steller; DASH, Das; Observ., observation and Std. Dev., standard deviation.

Table 2. QR estimates for crude oil and cryptocurrencies returns

	BTC	BTC.D1	BTC.D4	BTC.D6	ETH	ETH.D1	ETH.D4	ETH.D6	LTC	LTC.D1	LTC.D4	LTC.D6
Quantile	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.
0.05	0.0624	0.0267	0.0425	0.2895^a	−0.0004	−0.0456^b	−0.0381^b	0.1928^a	0.0400	0.0193	0.0233	0.1799^a
0.10	0.0255	0.0350	0.0803^a	0.2416^a	0.0035	−0.0353^b	−0.0471^a	0.1671^a	0.0185	0.0080	0.0610^a	0.1465^a
0.15	0.0296	0.0142	0.0843^a	0.1796^a	−0.0059	−0.0179	−0.0205	0.1101^a	−0.0011	−0.0005	0.0662^a	0.1051^a
0.20	0.0072	0.0252	0.0822^a	0.1378^a	−0.0039	−0.0097	0.0000	0.0962^a	0.0064	0.0135	0.0544^a	0.0963^a
0.25	0.0067	0.0203	0.0850^a	0.1172^a	0.0025	−0.0014	0.0124	0.0905^a	0.0143	0.0107	0.0495^a	0.1075^a
0.30	0.0004	0.0056	0.0781^a	0.1008^a	−0.0042	−0.0028	0.0238^c	0.0828^a	0.0114	0.0093	0.0415^a	0.1047^a
0.35	0.0013	−0.0074	0.0830^a	0.0837^a	−0.0080	−0.0073	0.0292^b	0.0677^a	0.0135	0.0062	0.0491^a	0.0983^a
0.40	−0.0225	0.0119	0.0990^a	0.0659	−0.0092	−0.0024	0.0369^a	0.0517^a	0.0069	0.0074	0.0607^a	0.1044^a
0.45	−0.0126	0.0138	0.1018^a	0.0659^a	−0.0053	0.0019	0.0321^b	0.0337^a	0.0036	0.0096	0.0582^a	0.1056^a
0.50	−0.0145	0.0030	0.0999^a	0.0841^a	−0.0068	0.0023	0.0258^c	0.0342^a	0.0032	0.0119	0.0520^a	0.0925^a
0.55	−0.0044	0.0054	0.1017^a	0.1024^a	−0.0018	0.0032	0.0257^c	0.0329^a	0.0069	0.0085	0.0442^a	0.1052^a
0.60	−0.0021	0.0004	0.0896^a	0.1285^a	−0.0027	−0.0045	0.0234^b	0.0416^a	0.0060	0.0036	0.0383^a	0.1235^a
0.65	0.0017	0.0148	0.0924^a	0.1579^a	−0.0126	−0.0054	0.0316	0.0435^a	0.0032	−0.0048	0.0432^a	0.1514^a
0.70	−0.0047	0.0074	0.0997^a	0.1774^a	−0.0096	−0.0138	0.0147	0.0572^a	0.0027	0.0025	0.0432^a	0.1602^a
0.75	0.0111	0.0110	0.1081^a	0.1935^a	0.0066	−0.0168	0.0127	0.0696^a	0.0128	0.0013	0.0493^a	0.1492^a
0.80	0.0040	0.0140	0.1239^a	0.2332^a	0.0068	−0.0231	0.0020	0.0806^a	0.0142	0.0004	0.0562^a	0.1446^a
0.85	−0.0153	0.0229	0.1103^a	0.2564^a	−0.0065	−0.0266	0.0035	0.0863^a	0.0024	0.0041	0.0493^a	0.1566^a
0.90	−0.0375	0.0352	0.0931^a	0.2013^a	−0.0224	−0.0209	−0.0054	0.1006^a	0.0041	0.0215	0.0248	0.1950^a
0.95	0.0075	0.0451	0.0210	0.0985	−0.0233	−0.0249	−0.0253^c	0.1008^a	0.0097	−0.0296	−0.0291^a	0.1377^a

Note: Entries with ^a, (^b) and [^c] indicate significance at the 1%, (5%) and [10%] level. BTC, Bitcoin; ETH, Ethereum; LTC, Litecoin.

Table 3. QQR estimates for crude oil and cryptocurrency returns

	BTC	BTC.D1	BTC.D4	BTC.D6	ETH	ETH.D1	ETH.D4	ETH.D6	LTC	LTC.D1	LTC.D4	LTC.D6
Quantile	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.	Coef.
0.05	−0.2075	−0.1473	−0.0339	−0.0141	−0.2917	−0.2025	−0.0512	−0.0281	−0.3952	−0.2479	−0.0503	−0.0186
0.10	−0.1835	−0.1310	−0.0296	−0.0124	−0.2526	−0.1803	−0.0444	−0.0250	−0.3448	−0.2174	−0.0430	−0.0161
0.15	−0.1595	−0.1147	−0.0253	−0.0108	−0.2135	−0.1580	−0.0377	−0.0219	−0.2945	−0.1869	−0.0358	−0.0136
0.20	−0.1354	−0.0985	−0.0210	−0.0091	−0.1744	−0.1358	−0.0309	−0.0187	−0.2442	−0.1564	−0.0285	−0.0111
0.25	−0.1114	−0.0822	−0.0167	−0.0075	−0.1353	−0.1136	−0.0242	−0.0156	−0.1939	−0.1259	−0.0213	−0.0086
0.30	−0.0873	−0.0659	−0.0124	−0.0058	−0.0962	−0.0914	−0.0174	−0.0125	−0.1436	−0.0955	−0.0140	−0.0061
0.35	−0.0633	−0.0496	−0.0081	−0.0042	−0.0570	−0.0692	−0.0107	−0.0094	−0.0933	−0.0650	−0.0067	−0.0036
0.40	−0.0393	−0.0334	−0.0038	−0.0026	−0.0179	−0.0470	−0.0039	−0.0062	−0.0430	−0.0345	0.0005	−0.0011
0.45	−0.0152	−0.0171	0.0005	−0.0009	0.0212	−0.0247	0.0028	−0.0031	0.0073	−0.0040	0.0078	0.0014
0.50	0.0088	−0.0008	0.0048	0.0007	0.0603	−0.0025	0.0096	0.0000	0.0576	0.0265	0.0150	0.0039
0.55	0.0328	0.0155	0.0091	0.0024	0.0994	0.0197	0.0163	0.0032	0.1079	0.0570	0.0223	0.0064
0.60	0.0569	0.0317	0.0134	0.0040	0.1385	0.0419	0.0231	0.0063	0.1582	0.0875	0.0296	0.0089
0.65	0.0809	0.0480	0.0177	0.0057	0.1776	0.0641	0.0298	0.0094	0.2085	0.1180	0.0368	0.0114
0.70	0.1049	0.0643	0.0220	0.0073	0.2168	0.0863	0.0366	0.0126	0.2588	0.1484	0.0441	0.0139
0.75	0.1290	0.0806	0.0263	0.0090	0.2559	0.1086	0.0433	0.0157	0.3091	0.1789	0.0513	0.0163
0.80	0.1530	0.0968	0.0306	0.0106	0.2950	0.1308	0.0501	0.0188	0.3594	0.2094	0.0586	0.0188
0.85	0.1770	0.1131	0.0349	0.0122	0.3341	0.1530	0.0568	0.0219	0.4097	0.2399	0.0659	0.0213
0.90	0.2011	0.1294	0.0392	0.0139	0.3732	0.1752	0.0636	0.0251	0.4600	0.2704	0.0731	0.0238
0.95	0.2251	0.1457	0.0435	0.0155	0.4123	0.1974	0.0703	0.0282	0.5103	0.3009	0.0804	0.0263

Note: BTC, Bitcoin; ETH, Ethereum; LTC, Litecoin

Figure A1. Plot of QR and QQR coefficients of crude oil and cryptocurrencies.

Figure A1. Continued.

Figure A1. Continued.

Figure A1. Continued.

Figure A1. Continued.

Figure A2. Time series plots of crude oil and cryptocurrency returns.

Figure A2. Continued.