Asymptotic Normality of the Estimators for Fractional Brownian Motions with Discrete Data

Table 2

The estimation results of comparative methods for sample size 𝑁=100.

Estimation method	Statistic	True values of 𝐻
		0.5600	0.6200	0.8500	0.9200
R/S method	Mean	0.53625	0.60581	0.83751	0.89032
	S.D.	0.37218	0.32670	0.36258	0.36521
	√MSE	0.37294	0.32701	0.36280	0.36641
	CPU time	50	48	49	50
Variations estimators	Mean	0.58002	0.63370	0.86261	0.93143
	S.D.	0.01606	0.01952	0.01910	0.03162
	√MSE	0.02567	0.02385	0.02289	0.03362
	CPU time	21	18	19	22
Wavelet method	Mean	0.56497	0.62951	0.86232	0.91931
	S.D.	0.01268	0.01497	0.05436	0.07484
	√MSE	0.01362	0.01774	0.05574	0.07484
	CPU time	100	108	112	118
Our method	Mean	0.56003	0.62003	0.85003	0.92007
	S.D.	0.00214	0.00967	0.01470	0.00948
	√MSE	0.00215	0.00968	0.01472	0.00949
	CPU time	15	13	21	24