Does volatility in cryptocurrencies drive the interconnectedness between the cryptocurrencies market? Insights from wavelets

Figures & data

Figure 1. Price (left) and returns (right) series of cryptocurrencies and VCRIX.

Table 1. Descriptive statistics

Statistic	BTC	BTCC	ETH	LTC	TETH	VCRIX	XRP
Mean	0.0022	0.0005	0.0022	−0.0001	0.0000	−0.0001	0.0016
Std. dev.	0.0485	0.0833	0.0619	0.0628	0.0039	0.0622	0.0805
Skewness	−0.5679	0.2017	−0.9119	−0.2899	0.5813	1.9010	1.0754
Kurtosis	10.1165	10.5947	12.0594	8.6498	19.5872	30.1729	16.1200
Jarque-Bera	2410***	2684***	3964***	1497***	12,834***	34,944***	8205***

Note: [*], [**], and [***] indicate significance at “10%, 5% and 1%” levels respectively.

Table 2. Unconditional Correlation

Probability	BTC	BTCC	ETH	LTC	TETH	VCRIX	XRP
BTC	1.000
BTCC	−0.012	1.000
ETH	0.071**	0.026	1.000
LTC	0.034	−0.005	−0.016	1.000
TETH	0.015	0.043	0.080***	−0.043	1.000
VCRIX	0.004	0.027	0.026	0.014	0.060**	1.000
XRP	−0.009	0.061**	0.003	−0.003	−0.033	0.009	1.000

Note: [*], [**], and [***] indicate significance at “10%, 5% and 1%” levels respectively.

Table 3. Interpretation of time-scales and frequencies

Frequency	Scale	Meaning
wi1	2–4	intraweek scales
wi2	4–8	weekly scale
wi3	8–16	fortnightly scale
wi4	16–32	monthly scale
wi5	32–64	monthly to quarterly scale
wi6	64–128	quarterly to biannual scale
wi7	128–256	biannual to annual scale

Figure 2. Comovements between VCRIX and cryptocurrencies.

Figure 3. Bi- and Partial wavelet interconnectedness of cryptocurrencies and VCRIX.

Figure 3. (Continued)

Figure 4. Wavelet bivariate correlations matrix. The codes for the variables are BTCC (C1), BTC (C2), ETH (C3), LTC (C4), TETH (C5), XRP (C6) and VCRIX (C7).

Figure 5. Wavelet multiple correlations among cryptocurrencies and VCRIX. U-upper limits, L- lower (at 95% confidence interval).

Figure 6. Wavelet multiple cross-correlations among cryptocurrencies and VCRIX.

Table 4. Wavelet Multiple Correlations (WMC)

Scale	WMC “lower”	Correlation	WMC “upper”
1	0.1633	0.2431	0.3197
2	0.1114	0.2261	0.3348
3	0.5020	0.6170	0.7105
4	0.4591	0.6276	0.7525
5	0.6376	0.8027	0.8973
6	0.9154	0.9695	0.9892
7	0.9905	0.9983	0.9997

Table 5. Wavelet Multiple Cross Correlations (WMCC)

Scale	Localizations	Time Lag (months)	Leading/Lagging variable
1	0.4385	4	BTCC
2	0.3922	−1	XRP
3	0.6797	−4	ETH
4	0.7057	5	XRP
5	0.8170	5	ETH
6	0.9710	1	ETH
7	0.9988	−1	ETH

Figure 7. Wavelet bivariate correlations matrix. The codes for the variables are BTCC (C1), BTC (C2), ETH (C3), LTC (C4), TETH (C5), XRP (C6) and VCRIX (C7).

Figure 8. Wavelet multiple correlations among cryptocurrencies and VCRIX.

Table 6. Wavelet Multiple Correlations (WMC)

Scale	WMC “lower”	Correlation	WMC “upper”
1	0.0902	0.1902	0.2863
2	0.1042	0.2444	0.3751
3	0.4526	0.6009	0.7169
4	0.4519	0.6562	0.7950
5	0.6815	0.8538	0.9364
6	0.8607	0.9633	0.9907

Figure 9. Wavelet multiple cross-correlations among cryptocurrencies and VCRIX.

Table 7. Wavelet Multiple Cross Correlations (WMCC)

Scale	Localizations	Time Lag (months)	Leading/Lagging variable
1	0.2547	4	TETH
2	0.2827	3	TETH
3	0.6467	−5	ETH
4	0.7547	4	XRP
5	0.9149	3	BTCC
6	0.9704	3	ETH

Figure 10. Wavelet bivariate correlations matrix. The codes for the variables are BTCC (C1), BTC (C2), ETH (C3), LTC (C4), TETH (C5), XRP (C6) and VCRIX (C7).

Figure 11. Wavelet multiple correlations among cryptocurrencies and VCRIX.

Table 8. Wavelet Multiple Correlations (WMC)

Scale	WMC “lower”	Correlation	WMC “upper”
1	0.3054	0.4307	0.5413
2	0.3171	0.4901	0.6315
3	0.4064	0.6232	0.7735
4	0.6416	0.8334	0.9271
5	0.5385	0.8604	0.9632

Figure 12. Wavelet multiple cross-correlations among cryptocurrencies and VCRIX.

Table 9. Wavelet Multiple Cross Correlations (WMCC)

Scale	Localizations	Time Lag (months)	Leading/Lagging variable
1	0.5905	4	BTCC
2	0.4980	−1	XRP
3	0.7590	4	ETH
4	0.9022	−9	BTC
5	0.9577	−9	ETH