Table 3.

Higher-order moment dependencies

Statistics	BTC	EUR	JPY	CAN	GBP	RMB
A. Asymmetry and Clustering of Volatility
$T^{-1}\sum z_{t-1}{z}_t^2$	−0.4022	0.0602	0.0400	−0.0176	−0.1787	0.0066
	(0.0344)**	(0.0344)	(0.0344)	(0.0344)	(0.0344)**	(0.0344)
$T^{-1}\sum z_{t-2}{z}_t^2$	−0.1650	0.0279	−0.0095	−0.0371	0.0072	−0.046
	(0.0344)**	(0.0344)	(0.0344)	(0.0344)	(0.0344)	(0.0344)
$T^{-1}\sum \left(z_{t-1}^2{z}_t^2-1\right)$	6.7558	0.4482	0.7333	0.3555	4.0713	1.988
	(0.0688)**	(0.0688)**	(0.0688)**	(0.0688)**	(0.0688)**	(0.0688)**
$T^{-1}\sum \left(z_{t-2}^2{z}_t^2-1\right)$	6.3798	0.2402	0.7133	0.2545	1.0178	0.7639
	(0.0688)**	(0.0688)**	(0.0688)**	(0.0688)**	(0.0688)**	(0.0688)**
B. Asymmetry and Clustering of Skewness
$T^{-1}\sum z_{t-1}^{}{z}_t^3$	2.7210	−0.1221	0.0110	0.2447	−0.2435	0.8140
	(0.0769)**	(0.0769)	(0.0769)	(0.0769)**	(0.0769)**	(0.0769)**
$T^{-1}\sum z_{t-2}^{}{z}_t^3$	−1.3565	0.2463	0.3341	−0.2610	−0.1503	0.3575
	(0.0769)**	(0.0769)**	(0.0769)**	(0.0769)**	(0.0769)	(0.0769)**
$T^{-1}\sum z_{t-1}^2{z}_t^3$	−29.9461	−1.3478	−0.7165	−1.4041	−25.0097	−6.5578
	(0.8939)**	(0.8939)	(0.8939)	(0.8939)	(0.8939)**	(0.8939)**
$T^{-1}\sum z_{t-2}^2{z}_t^3$	−35.5956	−0.7918	−1.2901	−0.7993	1.5333	−2.071
	(0.8939)**	(0.8939)	(0.8939)	(0.8939)	(0.8939)	(0.8939)*
C. Asymmetry and Clustering of Kurtosis
$T^{-1}\sum z_{t-1}^{}{z}_t^4$	−58.0522	0.2365	0.8508	−0.8733	17.6157	−3.3845
	(0.2036)**	(0.2036)	(0.2036)**	(0.2036)**	(0.2036)**	(0.2036)**
$T^{-1}\sum z_{t-2}^{}{z}_t^4$	20.8810	1.0294	−0.3219	−0.4130	4.8025	−1.7608
	(0.2036)**	(0.2036)**	(0.2036)	(0.2036)*	(0.2036)**	(0.2036)**
$T^{-1}\sum \left(z_{t-1}^2{z}_t^4-3\right)$	513.7123	5.4591	13.9450	6.8625	191.7277	43.0368
	(.3862)**	(0.3862)**	(0.3862)**	(0.3862)**	(0.3862)**	(0.3862)**
$T^{-1}\sum \left(z_{t-2}^2{z}_t^4-3\right)$	384.1675	4.3663	9.5722	3.3608	17.6863	14.5154
	(0.3862)**	(0.3862)**	(0.3862)**	(0.3862)**	(0.3862)**	(0.3862)**

Standardized returns are computed using the equation $z_t=\left(r_t-\widehat{\mu }\right)/\widehat{\sigma }$, where $\widehat{\mu }$ and $\widehat{\sigma }$ are estimated SGED mean and standard deviation of returns. The test statistics are computed using Equations (A1) to (A6). Parentheses include the standard errors of the test statistics

** and * indicate significance at the 1% and 5% levels, respectively