Fractional Brownian Motion & Hurst Exponent

H (set): 0.70 H (DFA): — H (R/S): — N: 1024
H=0.70
N=1024
1
fBm is characterized by H: H=0.5 = Brownian motion; H>0.5 = persistent (trending); H<0.5 = anti-persistent (mean-reverting). Var[B_H(t)] = t^(2H). DFA (Detrended Fluctuation Analysis) estimates H from scaling of RMS fluctuations vs. window size.