Table 2 Results of the Monte Carlo design to calculate the Hurst exponent with TA and KS-TA for fractional Brownian motions with different Hs and sizes
From: Improvement in Hurst exponent estimation and its application to financial markets
H | SIZE | TA | KS-TA | ||
|---|---|---|---|---|---|
MEAN | STD | MEAN | STD | ||
0.1 | \(2^{7}\) | 0.100 | 0.053 | 0.102 | 0.070 |
\(2^{10}\) | 0.100 | 0.014 | 0.100 | 0.015 | |
\(2^{15}\) | 0.100 | 0.006 | 0.100 | 0.003 | |
0.5 | \(2^{7}\) | 0.492 | 0.082 | 0.499 | 0.081 |
\(2^{10}\) | 0.499 | 0.034 | 0.501 | 0.027 | |
\(2^{15}\) | 0.499 | 0.014 | 0.500 | 0.006 | |
0.9 | \(2^{7}\) | 0.891 | 0.092 | 0.897 | 0.093 |
\(2^{10}\) | 0.897 | 0.039 | 0.901 | 0.030 | |
\(2^{15}\) | 0.899 | 0.016 | 0.900 | 0.007 | |