Table 1 Results of the Monte Carlo design to calculate the Hurst exponent with GHE(1) and KS-GHE(1) for fractional Brownian motions with different Hs and sizes
From: Improvement in Hurst exponent estimation and its application to financial markets
H | SIZE | GHE(1) | KS-GHE(1) | ||
|---|---|---|---|---|---|
MEAN | STD | MEAN | STD | ||
0.1 | \(2^7\) | 0.100 | 0.040 | 0.102 | 0.048 |
\(2^{10}\) | 0.100 | 0.017 | 0.100 | 0.014 | |
\(2^{15}\) | 0.100 | 0.007 | 0.100 | 0.004 | |
0.5 | \(2^7\) | 0.497 | 0.074 | 0.503 | 0.072 |
\(2^{10}\) | 0.497 | 0.041 | 0.499 | 0.029 | |
\(2^{15}\) | 0.498 | 0.020 | 0.499 | 0.009 | |
0.9 | \(2^7\) | 0.871 | 0.088 | 0.883 | 0.086 |
\(2^{10}\) | 0.882 | 0.063 | 0.891 | 0.054 | |
\(2^{15}\) | 0.889 | 0.043 | 0.896 | 0.033 | |