Parameter estimation for discretized geometric fractional Brownian motions with applications in Chinese financial markets

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Estimation results of the sampling interval \(h=1/12\) with different sample size

	The first group			The second group			The third group
	μ	H	σ	μ	H	σ	μ	H	σ
True value	0.2000	0.3500	0.3000	0.5000	0.5500	0.4000	0.8000	0.7500	0.5000
Panel A. Sample size N = 100
Panel A.1 The results of the method proposed in this paper
Mean	0.1811	0.3610	0.3234	0.5269	0.5685	0.3828	0.8241	0.7391	0.4833
S.Dev.	0.4025	0.2248	0.2816	0.3576	0.2962	0.3012	0.3044	0.3189	0.3217
CPU time	3			3			3
Panel A.2 The results of the method proposed in Xiao et al. [43]
Mean	0.1797	0.3207	0.3374	0.5303	0.5724	0.4261	0.7737	0.7799	0.5379
S.Dev.	0.4026	0.3918	0.4216	0.4060	0.3685	0.4012	0.3299	0.4042	0.3865
CPU time	19			21			22
Panel A.3 The results of the method proposed in Misiran et al. [31]
Mean	0.2359	0.3189	0.3467	0.5326	0.5809	0.4342	0.8594	0.7127	0.5785
S.Dev.	0.5277	0.5581	0.4242	0.5237	0.5366	0.5987	0.4055	0.4357	0.4087
CPU time	792			795			801
Panel B. Sample size N = 200
Panel B.1 The results of the method proposed in this paper
Mean	0.1947	0.3544	0.3135	0.4936	0.5540	0.4012	0.8118	0.7451	0.5055
S.Dev.	0.1178	0.1985	0.2076	0.1090	0.1377	0.1678	0.1624	0.1735	0.1887
CPU time	6			5			5
Panel B.2 The results of the method proposed in Xiao et al. [43]
Mean	0.1904	0.3559	0.3186	0.5140	0.5445	0.4196	0.8201	0.7591	0.5195
S.Dev.	0.2125	0.2199	0.2686	0.2810	0.2761	0.3225	0.2215	0.2541	0.2210
CPU time	35			36			40
Panel B.3 The results of the method proposed in Misiran et al. [31]
Mean	0.2153	0.3385	0.3201	0.5191	0.5389	0.4225	0.8291	0.7614	0.5236
S.Dev.	0.2615	0.3088	0.3190	0.3022	0.2911	0.3611	0.3196	0.3088	0.3257
CPU time	1687			1765			1973