Nonlinear Behaviors of Tail Dependence and Cross-Correlation of Financial Time Series Model

Table 2

Cross-correlation exponent ℎ_𝑥𝑦(𝑞) and multifractal scaling exponent 𝜛_𝑥𝑦(𝑞).

Data	Cross-correlation exponent ℎ𝑥𝑦(𝑞)			Multifractal scaling exponent 𝜛𝑥𝑦(𝑞)
𝑞	R.data	S.data1	S.data2	R.data	S.data1	S.data2
−10	0.8664	0.8425	0.8076	−8.8641	−8.8248	−8.5758
−9	0.8569	0.8321	0.8014	−7.9922	−7.9489	−7.7622
−8	0.8456	0.8196	0.7942	−7.1247	−7.0772	−6.9537
−7	0.8320	0.8045	0.7820	−6.2643	−6.2117	−6.1520
−6	0.8158	0.7860	0.7665	−5.4148	−5.3562	−5.3592
−5	0.7965	0.7634	0.7479	−4.5824	−4.5171	−4.5782
−4	0.7739	0.7364	0.7281	−3.7756	−3.7055	−3.8123
−3	0.7483	0.7060	0.7035	−3.0049	−2.9379	−3.0654
−2	0.7200	0.6748	0.6800	−2.2800	−2.2296	−2.3420
−1	0.6891	0.6447	0.6551	−1.6091	−1.5847	−1.6490
0	0.6507	0.6143	0.6252	−1	−1	−1
1	0.6172	0.5870	0.5972	−0.4628	−0.4730	−0.4128
2	0.5766	0.5590	0.5602	−0.0067	−0.0020	0.1004
3	0.5370	0.5321	0.5241	0.3711	0.4163	0.5423
4	0.5024	0.5072	0.4917	0.6898	0.7887	0.9269
5	0.4744	0.4848	0.4642	0.9722	1.1242	1.2710
6	0.4524	0.4653	0.4414	1.2346	1.4321	1.5886
7	0.4351	0.5486	0.4386	1.4858	1.7204	1.8893
8	0.4213	0.5344	0.4074	1.7306	1.9953	2.1793
9	0.4102	0.4224	0.3947	1.9715	2.2614	2.4622
10	0.4010	0.4122	0.3841	2.2097	2.5216	2.7405

Note: R.data means the real data; S.data1 and S.data2 denote two pairs of simulated data.