. 2022 Nov 30;10:933264. doi: 10.3389/fpubh.2022.933264

Table 3.

The results of three types of interactions for all the 10 paired markets.

	Stock-Oil	Stock-Gold	Stock-Currency		Stock-Cryptocurrency			Oil-Gold
	dj-wt	dj-go	dj-ch	dj-eu	dj-bi	dj-et	dj-li	wt-go
$ϕ_{12}^{B}$	−0.0067 (0.008)	−0.0365 (0.026)	0.0060 (0.002)^b	0.0807 (0.036)^b	0.0065 (0.003)^a	0.0020 (0.002)	−0.0021 (0.002)	0.0278 (0.073)
$ϕ_{21}^{B}$	0.1858 (0.072)^b	−0.0279 (0.023)	0.1121 (0.142)	−0.0010 (0.013)	0.4624 (0.117)^c	0.4998 (0.168)^c	0.5831 (0.172)^c	0.0081 (0.008)
$ϕ_{12}^{A}$	0.0177 (0.012)	−0.0185 (0.026)	−0.0204 (0.010)^b	−0.1593 (0.107)	0.0033 (0.010)	0.0070 (0.006)	0.0016 (0.006)	−0.1407 (0.117)
$ϕ_{21}^{A}$	0.1845 (0.122)	−0.0046 (0.014)	0.0315 (0.166)	0.0883 (0.012)^c	0.0011 (0.155)	0.0248 (0.186)	−0.0035 (0.176)	0.0053 (0.010)
$ν_{12}^{B}$	−0.0000 (0.001)	−0.0068 (0.005)	0.0001 (0.000)	−0.0793 (0.037)^b	−0.0007 (0.000)^c	−0.0001 (0.000)^b	−0.0003 (0.000)^c	0.2720 (0.098)^c
$ν_{21}^{B}$	0.2287 (0.073)^c	0.0024 (0.004)	−0.0114 (0.089)	0.0005 (0.000)	0.3676 (0.115)^c	1.5460 (0.387)^c	0.3039 (0.203)	−0.0000 (0.000)
$ν_{12}^{A}$	0.0006 (0.000)	0.0003 (0.001)	0.0009 (0.000)^a	0.1261 (0.135)	0.0001 (0.000)	0.0001 (0.000)	−0.0002 (0.000)	0.1408 (0.061)^b
$ν_{21}^{A}$	0.2365 (0.092)^b	−0.0003 (0.000)	0.1988 (0.098)^b	−0.0001 (0.000)	0.0581 (0.064)	−0.1074 (0.070)	−0.1464 (0.040)^c	−0.0001 (0.000)^c
$ω_{12}^{B}$	0.0187 (0.007)^c	0.0044 (0.010)	0.1160 (0.143)	−0.0163 (0.010)	−0.0042 (0.009)	0.0190 (0.015)	−0.0018 (0.016)	0.0380 (0.029)
$ω_{12}^{A}$	0.0319 (0.013)^b	−0.0587 (0.071)	0.2059 (0.400)	0.0789 (0.024)^c	0.0427 (0.028)	0.0650 (0.037)^a	0.0820 (0.053)	0.0529 (0.055)
	Oil-Currency		Oil-Cryptocurrency			Gold-Currency
	wt-ch	wt-eu	wt-bi	wt-et	wt-li	go-ch	go-eu	Sum (23)
$ϕ_{12}^{B}$	0.0038 (0.008)	−0.0611 (0.1198)	−0.0021 (0.012)	−0.0018 (0.009)	−0.0112 (0.009)	0.0033 (0.003)	0.1218 (0.045)^c	√ (4+, 1–)
$ϕ_{21}^{B}$	0.0312 (0.051)	4.8e−3 (5.0e-3)	−0.0603 (0.037)	0.0722 (0.089)	−0.0437 (0.051)	0.1355 (0.123)	−0.0195 (0.015)	√ (4+, 1–)
$ϕ_{12}^{A}$	−0.0203 (0.026)	−0.3245 (0.2592)	0.0539 (0.020)^c	0.0523 (0.014)^c	0.0379 (0.013)^c	0.0022 (0.010)	0.2007 (0.145)	√ (3+, 1–)
$ϕ_{21}^{A}$	−0.0052 (0.035)	4.0e−3 (4.0e-3)	0.0464 (0.037)	0.0605 (0.046)	0.0278 (0.040)	0.0867 (0.214)	0.0453 (0.015)^c	√ (2+, 3–)
$ν_{12}^{B}$	−0.0022 (0.000)^c	−0.3760 (0.2530)	−0.0028 (0.000)^c	−0.0009 (0.000)	−0.0010 (0.000)^c	−0.0003 (0.000)^c	−0.0188 (0.026)	–(2+, 11–)
$ν_{21}^{B}$	−0.0643 (0.011)^c	−9.4e-6 (8.6e-5)	−0.0649 (0.006)^c	0.2885 (0.082)^c	−0.1007 (0.010)^c	−2.1056 (0.549)^c	0.0007 (0.001)	? (7+, 7–)
$ν_{12}^{A}$	−0.0034 (0.001)^b	−0.4156 (0.4453)	−0.0029 (0.001)^b	−0.0015 (0.000)	−0.0015 (0.000)^a	0.0009 (0.000)^c	0.1213 (0.082)	√ (7+, 3–)
$ν_{21}^{A}$	0.0017 (0.002)	−7.6e-6 (5.4e-6)	0.0010 (0.001)	0.0009 (0.002)	−0.0029 (0.000)^c	−0.5010 (0.287)^a	−0.0004 (0.000)	√ (2+, 8–)
$ω_{12}^{B}$	−0.0107 (0.017)	0.0282 (0.0214)	0.0047 (0.006)	1.3236 (0.762)^a	1.0298 (0.702)	−0.0051 (0.048)	0.0104 (0.002)^c	√ (3+)
$ω_{12}^{A}$	0.0667 (0.058)	0.0707 (0.0400)^a	−0.0076 (0.016)	1.1784 (1.235)	2.0265 (1.522)	0.0602 (0.149)	0.0154 (0.003)^c	√ (9+)
	Gold-Cryptocurrency		Currency-Cryptocurrency
	go-et	go-li	ch-bi	ch-et	ch-li	eu-bi	eu-et	eu-li
$ϕ_{12}^{B}$	0.0018 (0.003)	−0.0022 (0.003)	−0.0461 (0.027)^a	0.0198 (0.012)	−0.0175 (0.015)	−0.0008 (0.002)	0.0019 (0.001)	0.0007 (0.001)
$ϕ_{21}^{B}$	−0.1243 (0.235)	−0.1969 (0.138)	−0.0239 (0.022)	0.0173 (0.025)	−0.0005 (0.028)	−0.4442 (0.146)^c	−0.4571 (0.365)	−0.4242 (0.298)
$ϕ_{12}^{A}$	0.0056 (0.008)	0.0081 (0.009)	0.0572 (0.045)	0.0296 (0.036)	0.0415 (0.033)	0.0055 (0.004)	0.0048 (0.002)	0.0045 (0.003)
$ϕ_{21}^{A}$	−0.0877 (0.298)	−0.1287 (0.305)	−0.0836 (0.045)^a	−0.1409 (0.061)^b	−0.1100 (0.060)^a	−0.0822 (0.555)	−1.1027 (0.679)	0.2288 (0.843)
$ν_{12}^{B}$	0.0001 (0.000)	−0.0000 (0.000)^b	0.0189 (0.013)	−0.0117 (0.002)^c	−0.0122 (0.001)^c	−0.0000 (0.000)	0.0000 (0.000)^b	0.0000 (0.000)
$ν_{21}^{B}$	3.7669 (1.657)^b	−3.6602 (0.070)^c	0.0158 (0.010)	−0.0130 (0.014)	0.0182 (0.010)^a	−4.0122 (0.052)^c	20.3682 (7.573)^c	−6.6027 (1.575)^c
$ν_{12}^{A}$	0.0007 (0.000)^b	0.0002 (0.000)^b	0.0266 (0.015)^a	−0.0023 (0.004)	−0.0054 (0.005)	0.0000 (0.000)	0.0000 (0.000)^a	0.0000 (0.000)
$ν_{21}^{A}$	0.8376 (0.688)	−1.5903 (0.211)^c	0.0196 (0.012)	−0.0538 (0.023)^b	−0.0078 (0.016)	−4.1559 (0.329)^c	13.4004 (8.642)	−9.7810 (2.100)^c
$ω_{12}^{B}$	0.0913 (0.082)	0.0127 (0.015)	0.4129 (0.560)	−1.1339 (1.963)	0.0546 (0.161)	0.0138 (0.014)	0.0768 (0.087)	−0.1177 (0.123)
$ω_{12}^{A}$	0.2608 (0.295)	0.0843 (0.076)	1.0558 (1.051)	7.0116 (3.260)^b	0.4365 (0.424)	0.1779 (0.026)^c	0.5102 (0.288)^a	1.1506 (0.254)^c

1. “dj” denotes the Dow Jones index in the US stock market; “wt” and “go” represent the WTI crude oil and gold in the commodity market, respectively; “ch” and “eu” denote the Chinese yuan (CNY) and Euro in the currency market, respectively, and “bi,” “et,” and “li” denote the abbreviations of Bitcoin, Ethereum, and Litecoin in the cryptocurrency market, respectively. 2. The superscripts a, b, and c on a parameter estimate denote the parameter estimate is significant at the 10, 5, and 1% levels, respectively. 3. The superscript ‘B' on the parameters ‘ $ϕ_{12}^{B}$ , $ϕ_{21}^{B}$ , $ν_{12}^{B}$ , $ν_{21}^{B}$ , and $ω_{12}^{B}$ ' and the superscript ‘A' on the parameters ‘ $ϕ_{12}^{A}$ , $ϕ_{21}^{A}$ , $ν_{12}^{A}$ , $ν_{21}^{A}$ , and $ω_{12}^{A}$ ' denote that the parameters are corresponding to the pre-COVID-19 and post-COVID-19 periods, respectively. 4. The symbol “+” (respectively, “–”) in column “Sum” denotes a financial feature corresponding to a parameter that is positively (respectively, negatively) significant when taking all ten paired markets as a whole. That is, the total number of pairs of assets that have a significantly positive or negative parameter value is greater than half of the sample size, respectively. In addition, the numbers inside a bracket beside the aforementioned symbol “+” or “–” denote the total number of pairs of assets that have a significantly positive or negative parameter value, respectively. 5. The symbol “√” in column “Sum” denotes a financial feature corresponding to a parameter that is slightly significant when taking all ten paired markets as a whole. That is, the total number of pairs of assets that have a significantly positive or negative parameter value is less than half of the sample size. In addition, the numbers inside a bracket beside the aforementioned symbol “√” denote the total number of pairs of assets that have a significantly positive or negative parameter value, respectively. 6. The symbol “?” in column “Sum” denotes a financial feature corresponding to a parameter that is significant when taking all ten paired markets as a whole. However, whether this financial feature is significantly positive or negative cannot be concluded because the total number of pairs of assets that have a significantly positive and negative parameter value is equal, respectively.