Linear combination of power-law functions for detecting multiscaling using detrended fluctuation analysis

• A linear combination of power-law functions for adjusting DFA data is proposed.
• Different values of the scaling exponents are estimated by nonlinear least-squares fitting.
• Examples of crude oil market and heart rate variability are discussed.
• Transition from anti-correlated to correlated behavior was observed.

In many instances, the fluctuation function obtained from detrended fluctuation analysis (DFA) cannot be described by a uniform power-law function along scales. In fact, the manifestation of crossover scales may reflect the simultaneous action of different stochastic mechanisms displayed predominantly within certain scale ranges. This note proposes the use of a linear combination of power-law functions for adjusting DFA data. The idea is that each power-law function recast the dominance of certain stochastic mechanisms (e.g., the mean-reversion and long-term trends) at specific scale domains. Different values of the scaling exponents are numerically estimated by means of a nonlinear least-squares fitting of power-law functions. Examples of crude oil market and heart rate variability are discussed with some detail for illustrating the advantages of taking a linear combination of power-law functions for describing scaling behavior from DFA.