Research Article
Asymptotic Normality of the Estimators for Fractional Brownian Motions with Discrete Data
Table 1
The estimation results of comparative methods for sample size
.
| Estimation method | Statistic
| True values of | 0.5600 | 0.6200 | 0.8500 | 0.9200 |
| R/S method | Mean | 0.50506 | 0.59232 | 0.82667 | 0.87692 | S.D. | 0.62322 | 0.43601 | 0.48195 | 0.51479 | | 0.62564 | 0.43689 | 0.48251 | 0.51659 | CPU time | 13 | 15 | 18 | 20 |
| Variations estimators | Mean | 0.59451 | 0.65676 | 0.89267 | 0.92050 | S.D. | 0.12365 | 0.23050 | 0.23739 | 0.15369 | | 0.12838 | 0.23341 | 0.24119 | 0.15369 | CPU time | 3 | 5 | 4 | 6 |
| Wavelet method | Mean | 0.58500 | 0.63520 | 0.87150 | 0.92963 | S.D. | 0.04265 | 0.02518 | 0.06251 | 0.09654 | | 0.04944 | 0.02941 | 0.06610 | 0.09702 | CPU time | 22 | 27 | 28 | 28 |
| Our method | Mean | 0.56667 | 0.62905 | 0.85507 | 0.92102 | S.D. | 0.03319 | 0.03092 | 0.01350 | 0.01325 | | 0.03385 | 0.03222 | 0.01442 | 0.01329 | CPU time | 3 | 3 | 5 | 5 |
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