Figure 7.

Weights for combining DFA₁ and DFA₂ estimates. The weighted estimate, α^w(q,n), is a linear combination of DFA₁ coefficients, α¹(q,n), and DFA₂ coefficients, α²(q,n), and it is proposed if there are no specific reasons to prefer one of the two detrending orders and if the time-series dynamics is assumed to be composed by fractional Gaussian noises or fractional Brownian motions. The weights, based on Equations (23), range between 0 (yellow) and 1 (dark blue). When n ≤ 12, α^w = α¹ for all q values; when n≥24, α^w = α¹ for q = 5, α^w = α² for q = −5, and α¹ and α² weights change linearly with q between −5 and +5 so that α^w is the average between α¹ and α² for q = 0. The α¹ and α² weights change linearly also with n between 12 and 24.