Connectedness of cryptocurrencies and gold returns: Evidence from frequency-dependent quantile regressions

Figures & data

Table 1. Summary of sample data

Cryptocurrency	Period	No. of IMFs
Bitcoin (BTC)	30/04/2013–18/04/2019	10
Dash (DASH)	17/02/2014–18/04/2019	10
Ethereum (ETH)	10/08/2015–18/04/2019	10
Litecoin (LTC)	30/02/2014–18/04/2019	10
Monero (XMR)	22/05/2014–18/04/2019	10
NEM (XEM)	02/04/2015–18/04/2019	10
Ripple (XRP)	05/08/2013–18/04/2019	10
Stellar (XLM)	06/08/2014–18/04/2019	10

Cryptocurrencies are arranged in alphabetical order.

Table 2. Summary statistics and stationarity tests of gold and cryptocurrencies returns and their IMFs

Statistic	Gold	BTC	Gold_IMF1	Gold _IMF5	Gold _IMFR	BTC_IMF1	BTC_IMF5	BTC_IMFR
Obs.	1500	1500	1500	1500	1500	1500	1500	1500
Mean	−0.0001	0.0016	0.000	−0.0001	−0.0002	0.0003	0.001	0.001
Std. Dev.	0.01	0.05	0.01	0.00	0.00	0.04	0.01	0.00
Skewness	0.03	−0.14	−0.05	0.07	−1.16	0.02	0.53	−0.91
Kurtosis	3.95	7.99	0.75	0.31	0.28	5.32	2.67	−0.47
Normtest.W*	0.96	0.88	0.99	1.00	0.84	0.94	0.91	0.84
ADF	−28.40*	−26.80*	−45.50*	−61.36*	−0.50	−48.10*	−39.08*	−46.74*
	Gold	DASH	Gold_IMF1	Gold _IMF5	Gold _IMFR	DASH_IMF1	DASH_IMF5	DASH_IMFR
Obs.	1299	1299	1299	1299	1299	1299	1299	1299
Mean	0.00	0.0031	0.00	0.00	0.00	−0.0004	−0.0009	0.0038
Std. Dev.	0.01	0.08	0.01	0.00	0.00	0.06	0.01	0.01
Skewness	0.20	3.32	−0.04	0.08	−0.94	0.39	−1.53	0.54
Kurtosis	2.47	49.06	0.45	0.43	−0.42	14.90	10.43	−0.96
Normtest.W*	0.97	0.77	0.99	1.00	0.83	0.88	0.81	0.91
ADF	−26.10*	−28.10*	−43.80*	−66.87*	1.76	−39.40*	−47.04*	−31.80*
	Gold	ETH	Gold_IMF1	Gold _IMF5	Gold _IMFR	ETH_IMF1	ETH_IMF5	ETH_IMFR
Obs.	928	928	928	928	928	928	928	928
Mean	0.0002	0.0036	0.0001	0.00	0.00	−0.0002	−0.0007	0.0047
Std. Dev.	0.008	0.0708	0.0063	0.001	3.00E-04	0.052	0.0124	0.0074
Skewness	0.366	0.635	−0.074	0.086	0.516	0.081	−0.196	0.595
Kurtosis	2.939	4.173	0.575	0.270	−1.027	1.039	1.661	−0.900
Normtest.W*	0.965	0.930	0.995	0.996	0.908	0.991	0.975	0.905
ADF	−22.30*	−21.30*	−37.10*	−54.10*	−1.52	−35.80*	−38.10*	−64.78*
	Gold	LTC	Gold_IMF1	Gold _IMF5	Gold _IMFR	LTC_IMF1	LTC_IMF5	LTC_IMFR
Obs.	1500	1500	1500	1500	1500	1500	1500	1500
Mean	−0.0001	0.0006	0.00	−0.0001	−0.0002	0.0007	0.0002	0.0002
Std. Dev.	0.01	0.07	0.01	0.00	0.00	0.05	0.01	0.00
Skewness	0.03	1.84	−0.05	0.07	−1.16	−0.02	0.05	0.03
Kurtosis	3.95	24.58	0.75	0.31	0.28	8.16	5.38	−1.24
Normtest.W*	0.96	0.77	0.99	1.00	0.84	0.89	0.88	0.95
ADF	−28.40*	−26.90*	−45.50*	−61.63*	0.50	−42.60*	−71.40*	−5.31*
	Gold	XMR	Gold_IMF1	Gold _IMF5	Gold _IMFR	XMR _IMF1	XMR _IMF5	XMR _IMFR
Obs.	1233	1233	1233	1233	1233	1233	1233	1233
Mean	0.00	−0.0001	0.0001	−0.0001	−0.0001	−0.0003	0.00	−0.0022
Std. Dev.	0.01	0.08	0.01	0.00	0.00	0.06	0.01	0.01
Skewness	0.21	0.36	−0.06	0.09	−0.96	0.05	0.09	−0.59
Kurtosis	2.60	4.85	0.55	0.51	0.00	1.50	0.37	−0.92
Normtest.W*	0.97	0.93	0.99	0.99	0.88	0.98	0.99	0.91
ADF	−25.50*	−27.70*	−43.00*	−64.06*	1.43	−42.90*	−52.83*	−41.45*
	Gold	XEM	Gold_IMF1	Gold _IMF5	Gold _IMFR	XEM_IMF1	XEM_IMF5	XEM_IMFR
Obs.	1016	1016	1016	1016	1016	1016	1016	1016
Mean	0.0001	0.0053	0.00	0.00	0.00	−0.0005	0.00	0.0077
Std. Dev.	0.01	0.09	0.01	0.00	0.00	0.07	0.02	0.01
Skewness	0.33	2.05	−0.05	0.05	−0.47	−0.09	0.10	−1.03
Kurtosis	2.76	18.10	0.43	−0.22	−1.24	3.81	1.82	−0.13
Normtest.W*	0.97	0.86	1.00	1.00	0.88	0.96	0.96	0.85
ADF	−23.40*	−23.70*	−38.70*	−57.55*	−3.73*	−34.60*	−60.34*	−125.23*
	Gold	XLM	Gold_IMF1	Gold _IMF5	Gold _IMFR	XLM_IMF1	XLM_IMF5	XLM_IMFR
Obs.	1181	1181	1181	1181	1181	1181	1181	1181
Mean	0.00	0.0017	0.0001	−0.0001	0.00	−0.0005	0.0003	0.0028
Std. Dev.	0.008	0.080	0.006	0.001	0.000	0.062	0.014	0.003
Skewness	0.220	1.345	−0.050	0.012	−0.815	−0.132	0.224	−0.893
Kurtosis	2.612	10.710	0.518	0.540	−0.626	3.490	2.652	−0.501
Normtest.W*	0.969	0.868	0.995	0.993	0.857	0.954	0.947	0.841
ADF	−25.00*	−26.60*	−42.10*	−55.70*	0.16	−40.50*	−53.47*	−59.99*
	Gold	XRP	Gold_IMF1	Gold _IMF5	Gold _IMFR	XRP_IMF1	XRP_IMF5	XRP_IMFR
Obs.	1433	1433	1433	1433	1433	1433	1433	1433
Mean	0.00	0.0026	0.00	0.00	0.00	−0.0006	0.0004	0.0032
Std. Dev.	0.009	0.077	0.007	0.001	0.000	0.061	0.014	0.004
Skewness	0.249	2.124	−0.048	−0.013	−1.106	−0.047	0.426	1.181
Kurtosis	2.781	32.901	0.669	0.296	0.283	19.051	3.271	0.249
Normtest.W*	0.967	0.733	0.993	0.996	0.859	0.801	0.915	0.824
ADF	−28.10*	−25.80*	−43.80*	−61.45*	1.35	−39.60*	−51.56*	14.81

Normtest. W *Indicates Shapiro–Wilk test of normality which is rejected at all conventional levels of significance. For ADF * indicates stationarity at the 5% significance level.

Figure 1. Return and IMF plots of gold and cryptocurrencies.

Figure 2. Bi-directional gold and cryptos QR and QQR.

Figure 2. (Continued).

short-legendFigure A1.