DFA reveals long-range correlations in time series. The slope of log F(n) vs log n gives the Hurst exponent H. H=0.5 = uncorrelated, H>0.5 = persistent, H<0.5 = anti-persistent.
Controls
Target H: 0.80
Estimated H: —
Series length: —
DFA algorithm:
1. Integrate series: Y(k)=Σxᵢ
2. Divide into boxes of size n
3. Detrend each box (linear fit)
4. F(n) = RMS of residuals
F(n) ~ n^H
H = 0.5: white noise
H > 0.5: long memory (fGn)
H < 0.5: anti-persistent
Used in: heartbeat dynamics,
finance, climate, neuroscience