Efficiently Implementing the Maximum Likelihood Estimator for Hurst Exponent

Table 1

Accuracy comparison for four cases covering six approaches, each value representing the mean of mean-squared errors (MSEs) of 100 realizations over 13 Hurst exponents, simply denoted as mean mean-squared errors (MMSEs).

Cases	𝑁=128	𝑁=256	𝑁=512	𝑁=1024	𝑁=2048	𝑁=4096
C1	𝟏.𝟏𝟖𝐄−𝟎𝟑	𝟓.𝟓𝟐𝐄−𝟎𝟒	𝟐.𝟗𝟎𝐄−𝟎𝟒	𝟏.𝟓𝟏𝐄−𝟎𝟒	𝟕.𝟏𝟏𝐄−𝟎𝟓	3.73𝐸−05
C2	1.72𝐸−03	8.50𝐸−04	4.65𝐸−04	2.59𝐸−04	1.19𝐸−04	6.57𝐸−05
C3-A1^a	1.36𝐸−03	5.99𝐸−04	2.94𝐸−04	1.55𝐸−04	7.44𝐸−05	𝟑.𝟕𝟏𝐄−𝟎𝟓
C3-A2^a	1.35𝐸−03	6.04𝐸−04	2.94𝐸−04	1.57𝐸−04	7.45𝐸−05	3.74𝐸−05
C4-A1^a	2.51𝐸−03	1.15𝐸−03	5.18𝐸−04	2.97𝐸−04	1.38𝐸−04	6.76𝐸−05
C4-A2^a	2.49𝐸−03	1.15𝐸−03	5.19𝐸−04	2.98𝐸−04	1.38𝐸−04	6.81𝐸−05

aA1 denotes Approach 1 and A2 denotes Approach 2.