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 2 Estimation results of the sampling interval \(h=1/52\) 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	0.1893	0.3588	0.3204	0.5260	0.5667	0.3803	0.8209	0.7407	0.4817
S.Dev.	0.3213	0.2048	0.2804	0.3420	0.2795	0.2966	0.2980	0.3152	0.3213
CPU time	3			3			3
Panel A.2 The results of the method proposed in Xiao et al. [43]
Mean	0.1769	0.3306	0.3279	0.5291	0.5684	0.4217	0.7723	0.7529	0.5306
S.Dev.	0.3915	0.3862	0.4176	0.3974	0.3681	0.3944	0.3231	0.3858	0.3847
CPU time	20			19			21
Panel A.3 The results of the method proposed in Misiran et al. [31]
Mean	0.2306	0.3203	0.3408	0.5320	0.5781	0.4296	0.8404	0.7567	0.5492
S.Dev.	0.4139	0.4520	0.4301	0.4467	0.4521	0.4536	0.3935	0.3665	0.3844
CPU time	781			796			793
Panel B. Sample size N = 200
Panel B.1 The results of the method proposed in this paper
Mean	0.2046	0.3489	0.3103	0.5019	0.5485	0.3991	0.8101	0.7498	0.5043
S.Dev.	0.1121	0.1724	0.1679	0.0997	0.1104	0.1175	0.1335	0.1173	0.1272
CPU time	6			5			6
Panel B.2 The results of the method proposed in Xiao et al. [43]
Mean	0.1923	0.3521	0.3175	0.5113	0.5407	0.4162	0.8157	0.7562	0.5164
S.Dev.	0.2012	0.2016	0.2413	0.2788	0.2538	0.3192	0.1518	0.2381	0.2101
CPU time	37			40			42
Panel B.3 The results of the method proposed in Misiran et al. [31]
Mean	0.2122	0.3294	0.3179	0.5137	0.5340	0.4112	0.8128	0.7610	0.5223
S.Dev.	0.2255	0.2176	0.2651	0.2976	0.2578	0.3513	0.2965	0.2611	0.2156
CPU time	1809			1796			1806