Table 3 Results of the Monte Carlo design to calculate the Hurst exponent with FD4 and KS-FD4 for fractional Brownian motions with different Hs and sizes
From: Improvement in Hurst exponent estimation and its application to financial markets
H | SIZE | FD4 | KS-FD4 | ||
|---|---|---|---|---|---|
MEAN | STD | MEAN | STD | ||
0.1 | \(2^{7}\) | 0.186 | 0.013 | 0.198 | 0.011 |
\(2^{10}\) | 0.171 | 0.006 | 0.185 | 0.004 | |
\(2^{12}\) | 0.164 | 0.004 | 0.179 | 0.003 | |
0.5 | \(2^{7}\) | 0.520 | 0.034 | 0.526 | 0.027 |
\(2^{10}\) | 0.512 | 0.018 | 0.519 | 0.012 | |
\(2^{12}\) | 0.509 | 0.012 | 0.517 | 0.007 | |
0.9 | \(2^{7}\) | 0.903 | 0.070 | 0.901 | 0.057 |
\(2^{10}\) | 0.902 | 0.052 | 0.902 | 0.040 | |
\(2^{12}\) | 0.899 | 0.041 | 0.901 | 0.030 | |