Nexus between cryptocurrencies and global uncertainty: A quantile regression approach

Figures & data

Figure 1. Graphical representation of monthly prices/index and returns of cryptos and uncertainties.

Table 1. Descriptive statistics and preliminary analysis

	Cryptocurrencies							Uncertainties
Variables	Bitcoin	Dashcoin	Ethereum	Litecoin	Monero	Neo	Ripple	GU	VIX	OVX
Observation.	96	96	96	96	96	96	96	96	96	96
Mean	0.0484	0.0367	0.0830	0.0339	0.0644	0.0435	0.0300	−0.0011	−0.0008	−0.0019
Median	0.0580	−0.0148	0.0612	0.0109	0.0268	0.0000	−0.0674	−0.0277	−0.0210	−0.0246
Std. Dev.	0.3917	0.5940	0.5369	0.4636	0.3951	0.7070	1.0407	0.3486	0.1445	0.2531
Skewness	−0.2827	−0.0378	−0.5687	0.0964	0.6920	0.1331	0.5510	0.2938	0.5165	1.2107
Kurtosis	2.6210	1.4512	2.4600	0.7595	1.2618	1.8143	2.2455	0.7119	1.6386	4.022
Jarque-Bera	31.051***	9.490***	31.568***	2.944	15.071***	14.841***	39.705***	3.889**	16.315***	99.073***
ADF	−5.596***	−5.748***	−6.101***	−5.331***	−7.013***	−4.773***	−6.116***	−8.864***	−8.572***	−7.910***
PP	−18.470***	−18.045***	−13.135***	−15.307***	−12.770***	−15.822***	−13.729***	−14.980***	−19.37***	−10.90***
LB (12)	19.179	19.314	9.024	13.567	13.665	18.940	8.810	17.956	17.010	16.077

Notes: Table 1 highlights the descriptive of cryptos and uncertainty measure for the sampled period. JB is the Jarque-Bera normality test statistics. ADF and PP are the statistics of Dickey-Fuller and Phillips-Perron respectively. LBQ is the Ljung-Box tests for 12^th-order serial correlations for returns. (***), (**) and (*) indicate the statistical significance at 1%, 5%, and 10% levels, respectively.

Table 2. Correlation matrix of global uncertainties and cryptocurrencies

Variables	GU	VIX	OVX	Bitcoin	Dash	Ethereum	Litecoin	Monero	Neo	Ripple
GU	1.000
VIX	−0.017	1.000
OVX	−0.055	0.162*	1.000
Bitcoin	0.016	0.582***	−0.096	1.000
Dash	0.971***	−0.005	−0.051	0.012	1.000
ETH	0.974***	0.011	−0.031	0.031	0.977***	1.000
Litecoin	0.042	0.550***	−0.154	0.879	0.054	0.073	1.000
Monero	−0.962***	−0.015	0.034	−0.044	−0.945***	−0.976***	−0.071	1.000
Neo	0.947***	0.000	−0.049	0.002	0.989***	0.960***	0.043	−0.922***	1.000
Ripple	−0.013	0.420***	−0.109	0.669***	−0.014	0.008	0.773***	−0.013	−0.033	1.000

Note: ***, and () are in respect of p < 0.01, and insignificant respectively.

Table 3. OLS regression estimation results for crypto-uncertainty nexus

GU	Bitcoin	Dashcoin	Ethereum	Litecoin	Monero	Neo	Ripple
${\chi }_1$	0.018	1.654***	1.499***	0.056	−1.090***	1.922***	−0.020
${\sigma }_{\mathrm{M}}$	(0.117)	(0.043)	(0.036)	(0.138)	(0.032)	(0.067)	(0.164)
$\overline{{\mathrm{R}}^2}$	−0.011	0.941	0.948	−0.009	0.924	0.897	−0.011
T-test	0.152	38.822	41.184	0.407	−33.810	28.621	−0.124
DW	3.300	0.226**	2.889	2.978	3.122	2.170	2.702
B-G	3.316	2.246	2.835	3.124	2.752	1.178	2.294
B-P	13.709*	4.399	2.163	10.392	0.424	0.026	1.795

Note: This table contains estimates by regressing crypto returns (${\mathrm{Q}}_{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{p}\mathrm{t}}$) on the changes in global uncertainty returns ($\mathrm{G}\mathrm{U}{\mathrm{R}}_1$) using OLS. The first row reports the estimated coefficients, the value in parentheses are the standard errors of the estimates. DW, B-G, and B-P correspondingly represent Durbin Watson, Breusch-Godfrey, and Breusch-Pagan tests of autocorrelation and homoscedasticity. ***, ** and * indicates statistical significance at the 1%, 5%, and 10% levels respectively.

Table 4. Nexus between cryptocurrencies and global uncertainty via quantile regression

Panel A: OLS
Uncertainty		Bitcoin	Dashcoin	Ethereum	Litecoin	Monero	Neo	Ripple
	${\chi }_1$	0.018	1.654***	1.499***	0.056	−1.090***	1.922***	−0.020
	${\sigma }_{\mathrm{M}}$	(0.117)	(0.043)	(0.036)	(0.138)	(0.032)	(0.067)	(0.164)
Panel B: Quantile Regression
Lower quantiles (bearish market: pandemic, polarisations and crypto market crash)
0.05	${\chi }_1$	0.5995**	1.8008***	1.4281***	0.6713***	−1.0977***	2.1597***	0.3256
	${\sigma }_{\mathrm{M}}$	(0.2880)	(0.0956)	(0.1483)	(0.2062)	(0.0240)	(0.1418)	(0.2133)
	t-value	2.081	18.833	9.633	3.256	−45.833	15.229	1.527
0.10	${\chi }_1$	0.3574	1.7451***	1.4510***	0.5503	−1.1324***	2.0519***	0.3634
	${\sigma }_{\mathrm{M}}$	(0.2701)	(0.1147)	(0.1051)	(0.3071)	(0.0308)	(0.1773)	(0.3126)
	t-value	1.324	15.212	13.810	1.792	−36.738	11.573	1.162
0.25	${\chi }_1$	0.103	1.5756***	1.3460***	0.1739	−1.1387***	1.8032***	0.0920
	${\sigma }_{\mathrm{M}}$	(0.1039)	(0.1760)	(0.0696)	(0.1404)	(0.0434)	(0.2227)	(0.1400)
	t-value	0.991	9.024	19.329	1.239	−26.226	8.0960	0.657
Normal quantiles (normal market: stable market conditions absent pandemic, polarisations and crash)
0.50	${\chi }_1$	0.070	1.4835***	1.3314***	−0.0338	−1.1390***	1.5312***	−0.0402
	${\sigma }_{\mathrm{M}}$	(0.1179)	(0.1095)	(0.0320)	(0.1389)	(0.0672)	(0.1440)	(0.1606)
	t-value	0.568	13.542	41.649	−0.243	−16.941	10.637	−0.2501
0.60	${\chi }_1$	0.018	1.4948***	1.3375***	−0.029	−1.1191***	1.6920***	−0.0634
	${\sigma }_{\mathrm{M}}$	(0.1475)	(0.0762)	(0.0370)	(0.1614)	(0.0911)	(0.1388)	(0.1947)
	t-value	0.119	19.610	36.129	−0.180	−12.280	12.188	−0.326
0.70	${\chi }_1$	−0.154	1.5139***	1.3555***	−0.2160	−1.1007***	1.7835***	−0.2105
	${\sigma }_{\mathrm{M}}$	(0.1379)	(0.0725)	(0.0417)	(0.1787)	(0.0806)	(0.1372)	(0.2199)
	t-value	−1.114	20.886	32.522	−1.209	−13.651	13.002	−0.958
Panel B: Quantile Regression
Uncertainty		Bitcoin	Dashcoin	Ethereum	Litecoin	Monero	Neo	Ripple
Upper Quantiles (bullish market: periods of improved market conditions)
0.80	${\chi }_1$	−0.295	1.5779***	1.4027***	−0.3951	−1.1332	1.8815***	−0.5890**
	${\sigma }_{\mathrm{M}}$	(0.1986)	(0.0627)	(0.0916)	(0.2780)	(0.0865)	(0.1174)	(0.2694)
	t-value	−1.487	25.149	15.307	−1.421	−13.103	6.029	−2.186
0.90	${\chi }_1$	−0.644**	1.6296***	1.6722***	−0.6962	−1.0299***	1.9910	−0.686
	${\sigma }_{\mathrm{M}}$	(0.2508)	(0.0812)	(0.1311)	(0.4110)	(0.1327)	(0.2056)	(0.3789)
	t-value	−2.568	20.077	12.755	−1.694	−7.760	9.682	−1.810
0.95	${\chi }_1$	−0.778***	1.6990***	1.6881	−0.5611	−0.9123***	2.3670***	−0.3696
	${\sigma }_{\mathrm{M}}$	(0.1904)	(0.1228)	(0.0900)	(0.3760)	(0.1536)	(0.1914)	(0.7869)
	t-value	−4.087	13.834	18.763	−1.492	−5.941	12.369	−0.470

Crypto-GU estimation results via QR. Notes: t-value are the corresponding t-statistics of coefficients. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively whiles () represents the standard error of the QR coefficients.

Table 5. Nexus between cryptocurrencies and global uncertainty with VIX and OVX as control variables

Lower quantiles (bearish market: pandemic, polarisations and crypto market crash)
0.05	${\chi }_1$	0.2354	1.8074***	1.5180***	0.3192	−1.1057***	2.1373***	0.1953
	${\sigma }_{\mathrm{M}}$	(0.2314)	(0.1127)	(0.1832)	(0.2609)	(0.0194)	(0.1234)	(0.2420)
	t-value	1.017	16.036	8.288	1.223	−57.118	17.315	0.807
0.10	${\chi }_1$	0.1907	1.7453***	1.4571***	0.1838	−1.1110***	2.0483***	0.0757
	${\sigma }_{\mathrm{M}}$	(0.1796)	(0.1243)	(0.1148)	(0.1851)	(0.0269)	(0.1692)	(0.1765)
	t-value	1.062	14.040	12.688	0.993	−41.267	12.106	0.429
0.25	${\chi }_1$	0.0353	1.5483***	1.3524***	0.0416	−1.1537***	1.8049***	−0.0386
	${\sigma }_{\mathrm{M}}$	(0.5931)	(0.1640)	(0.0744)	(0.1236)	(0.0364)	(0.1968)	(0.1472)
	t-value	0.328	9.443	18.170	0.336	−31.722	9.170	−0.262
Normal quantiles (normal market: stable market conditions absent pandemic, polarisations and crash)
0.50	${\chi }_1$	−0.0647	1.4777***	1.3294***	0.0613	−1.1402***	1.5896***	−0.0924
	${\sigma }_{\mathrm{M}}$	(0.1164)	(0.1060)	(0.0362)	(0.1310)	(0.0753)	(0.1510)	(0.1465)
	t-value	−0.531	13.937	36.753	0.468	−15.141	10.527	−0.631
0.60	${\chi }_1$	−0.1473	1.4927***	1.3380***	−0.0516	−1.115***	1.6861***	−0.0571
	${\sigma }_{\mathrm{M}}$	(0.1332)	(0.0778)	(0.0329)	(0.1309)	(0.0752)	(0.1512)	(0.1449)
	t-value	−1.106	19.178	40.644	−0.3939	−14.824	11.153	−0.3940
0.70	${\chi }_1$	−0.0203	1.5033***	1.3581***	−0.0143	−1.1543***	1.7436***	−0.1041
	${\sigma }_{\mathrm{M}}$	(0.1546)	(0.0715)	(0.0461)	(0.1528)	(0.0783)	(0.1468)	(0.1756)
	t-value	−0.131	21.029	29.457	−0.0934	−14.746	11.896	−0.593
Upper Quantiles (bullish market: periods of improved market conditions)
0.80	${\chi }_1$	−0.0203	1.5921***	1.3979***	0.1876	−1.1429***	1.9320***	−0.1479
	${\sigma }_{\mathrm{M}}$	(0.1409)	(0.0646)	(0.0904)	(0.2057)	(0.0889)	(0.1259)	(0.2744)
	t-value	−0.144	24.648	15.463	0.912	−12.862	15.346	−0.539
0.90	${\chi }_1$	0.0274	1.6320***	1.6727***	0.4615	−1.0440	1.9939***	0.0672
Upper Quantiles (bullish market: periods of improved market conditions)
0.05	${\chi }_1$	0.2354	1.8074***	1.5180***	0.3192	−1.1057***	2.1373***	0.1953
	${\sigma }_{\mathrm{M}}$	(0.2248)	(0.0751)	(0.1330)	(0.3798)	(0.1362)	(0.1947)	(0.4958)
	t-value	0.122	21.742	12.573	1.215	−7.668	10.240	0.136
0.95	${\chi }_1$	−0.2554	1.7068***	1.6858***	−0.0996	−1.1232***	2.3523***	0.5731
	${\sigma }_{\mathrm{M}}$	(0.2456)	(0.1104)	(0.0825)	(0.4447)	(0.1418)	(0.1849)	(0.5915)
	t-value	−1.040	15.456	20.424	−0.2239	−7.921	12.723	0.969

Notes: Crypto-GU estimation results via QR with control variables (NVI and OVX). Notes: t-value is the corresponding t-statistics of coefficients. ***, **, and * indicate significance at 1%, 5%, and 10% levels, respectively whiles () represents the standard error of the QR coefficients.

Table 6. Crypto-GU estimations via QQR

QQR	Bitcoin	Dash	Ethereum	Litecoin	Monero	Neo	Ripple
quantiles ($\pi$)
0.05	−0.0918	0.9126	0.6472	0.4485	−1.4365	0.2160	0.0140
0.10	−0.0918	0.9126	0.6472	0.4485	−1.4365	0.2160	0.0140
0.15	0.4867	0.5422	0.4181	0.6323	−0.8079	0.4631	0.6692
0.20	0.6601	0.8418	0.3373	−0.4818	−0.8665	1.5894	0.2210
0.25	−0.5234	0.8434	0.3874	−0.3568	−0.7971	0.8843	−0.7000
0.30	0.4736	1.6564	0.3357	0.9303	−0.4942	0.3717	−0.2397
0.35	0.0236	1.1649	1.3159	0.5528	−1.1700	0.3171	−0.3191
0.40	−0.8344	1.5096	1.2863	−0.7249	−0.4467	0.3155	−0.0006
0.45	0.0256	0.9571	1.2210	0.18889	−1.0538	0.2443	−0.3099
0.50	0.5972	1.1276	1.2625	0.5069	−0.8413	0.0747	0.4456
0.55	0.6733	0.8080	1.3298	0.3282	−0.6257	1.5927	0.4742
0.60	−0.5910	1.4894	1.3029	−0.2687	−1.2071	1.7733	−0.4068
0.65	0.1644	0.7456	0.6403	0.5361	−1.8929	0.8917	0.0564
0.70	−0.1704	0.8016	0.5897	0.6521	−0.8368	1.0213	−0.0231
0.75	−0.6126	0.5642	0.2158	−0.3160	−0.1736	0.3219	−0.1056
0.80	−0.0809	1.7115	0.5343	−0.3249	−0.5426	1.2231	0.0301
0.85	−0.0439	0.3546	0.6096	0.1746	−0.0338	0.1684	−0.6131
0.90	1.0296	1.0296	0.6510	0.3498	−0.6087	1.2163	0.4995
0.95	−1.0537	1.9132	0.5081	−0.8632	−0.1662	0.9088	−0.0198

Notes: The mean conditioned interactions (collectively referred to as QQR) regarding the returns of GU and cryptos are presented in Table 5. The non-parameterized model, however, fails to incorporate the statistical significance of the QQR components into account. As a consequence, the QQR results receive validation utilising the QR projections. The factor $\pi$ denotes quantiles in this context. For convenience and conciseness, and considering the wide-ranging scope of the comprehensive computation, we skimmed every projection to account for comprehensive crypto-GU circulations.

Figure 2. Line-based visualisation of QR and QQR projections (cryptos-GU nexus)s.

Table 7. Results of Residual-based LaGrange multiplier (LM) autocorrelation test for QR

quantiles ($\pi$)	Bitcoin	Dash	Ethereum	Litecoin	Monero	Neo	Ripple
0.05	4.097	4.4234	5.3329	3.2595	2.4323	4.4521	1.261
	(0.1009)	(0.1095)	(0.0695)	(0.1960)	(0.2964)	(0.1080)	(0.0936)
0.10	3.189	4.2806	4.5344	2.0691	1.9741	2.5121	3.599
	(0.0514)	(0.1176)	(0.1036)	(0.3554)	(0.3727)	(0.0785)	(0.1211)
0.25	4.472	4.3722	4.4752	4.2018	4.2018	2.4672	2.4672
	(0.0988)	(0.1088)	(0.0924)	(0.1223)	(0.1223)	(0.0539)	(0.1339)
0.50	21.834***	6.2217	5.0265	3.3143	2.2727	3.7368	19.040***
	(0.0000)	(0.05457)	(0.0810)	(0.1907)	(0.3210)	(0.0877)	(0.0000)
0.60	21.022***	5.9199	3.4308	4.5428	2.2604	1.0665	17.961***
	(0.0000)	(0.0518)	(0.1799)	(0.1032)	(0.3230)	(0.2108)	(0.0001)
0.70	21.059***	4.2591	3.8083	3.4315	2.4207	2.7387	15.884***
	(0.0000)	(0.0765)	(0.1489)	(0.1798)	(0.2981)	(0.0809)	(0.0004)
0.80	2.853	5.1049	4.5343	1.6747	3.4174	5.0198	2.113
	(0.1049)	(0.0779)	(0.1036)	(0.4329)	(0.1811)	(0.0813)	(0.1023)
0.90	3.269	5.4571	3.8369	0.7644	3.5401	3.9019	4.2985
	(0.0621)	(0.0653)	(0.1468)	(0.6824)	(0.1703)	(0.1421)	(0.0696)
0.95	2.129	4.6396	2.0502	0.9298	2.8409	3.6825	3.668
	(0.1023)	(0.0923)	(0.0886)	(0.6282)	(0.2416)	(0.1586)	(0.0548)

Note: The figures enclosed in parentheses denote the p-values associated with the test statistics at a significance level of 5%. If the p-value is smaller than the chosen significance level (alpha), we reject the null hypothesis, indicating the presence of autocorrelation in the model. Conversely, if the p-value exceeds the significance level, we do not reject the null hypothesis, signifying the absence of autocorrelation within the model.

Figure 3a. Causality-in-mean test.

Figure 3b. Causality-in-variance test.

Table 8. Results of causality in mean and variance test

quantiles ($\pi$)	Bitcoin	Dash	Ethereum	Litecoin	Monero	Neo	Ripple
0.10 ($\mu$)	1.2035	1.3143	0.9698	0.9269	1.4615	2.0632**	1.6885*
$\sigma$	5.8916***	3.4890***	5.3408***	5.7176***	3.7093***	15.0533***	7.1196***
0.15 ($\mu$)	1.0728	1.6401*	1.3614	1.5464	1.8169*	2.0219**	1.6107*
$\sigma$	5.0473***	3.1089***	5.0938***	4.5657***	2.9724***	11.7938***	6.2126***
0.25 ($\mu$)	1.1301	1.9631**	1.1130	1.4150	2.2646**	8.6878***	1.3740
$\sigma$	4.0811***	2.9690***	5.0320***	4.1782***	3.6246***	7.9010***	4.9216***
0.50 ($\mu$)	1.4020	1.9436**	1.8767*	1.1077	2.4081**	4.3345***	1.4080
$\sigma$	3.3372***	2.6515***	3.1496***	3.3783***	2.7512***	3.9614***	3.1813***
0.60 ($\mu$)	1.7117*	1.5639	1.6307*	1.1778	1.8259*	3.1506***	1.3050
$\sigma$	2.7715***	2.2211**	2.7427***	2.9505***	2.5989***	2.7418***	2.6086***
0.70 ($\mu$)	1.4902	1.4484	1.7230*	1.3882	1.7954*	2.4852***	1.3189
$\sigma$	2.2471***	1.8672*	1.9487*	2.3212**	2.0680**	1.9730*	2.1872**
0.80 ($\mu$)	1.2434	1.3951	0.9558	0.8830	1.4938	1.4394	1.0729
$\sigma$	2.0542***	1.333	1.1270	1.3793	1.4951	1.3039	1.4547
0.90 ($\mu$)	0.6845	0.5520	0.5393	0.7283	0.5760	0.8016	0.6236
$\sigma$	0.9962	0.4109	0.8205	1.3951	0.4485	0.9916	1.0098

Note: $\mu$ and $\sigma$ represent the causality in mean and variance respectively. [*], [**], and [***] denote the significance levels for the critical values of 1.645, 1.96, and 2.567 respectively. If the test statistics is greater than the established critical value, we reject the null hypothesis of no Granger causality, else we fail to reject.