Effect of trends on detrended fluctuation analysis

Area of Science:

• Signal processing
• Statistical physics
• Time series analysis

Background:

• Detrended fluctuation analysis (DFA) is crucial for quantifying long-range correlations in noisy signals.
• Real-world data often contains trends, complicating standard DFA scaling analysis.
• Understanding trend effects is vital for accurate interpretation of signal dynamics.

Purpose of the Study:

• To systematically investigate the impact of linear, periodic, and power-law trends on DFA results.
• To elucidate the mechanisms behind trend-induced crossovers in scaling behavior.
• To provide methods for appropriate DFA application in the presence of trends.

Main Methods:

• Simulating correlated noise with various trend types (linear, periodic, power-law).
• Comparing DFA scaling results for noise with and without trends.
• Analyzing the dependence of crossover characteristics on trend and noise parameters.
• Investigating the superposition principle for DFA of trended signals.

Main Results:

• Trends introduce apparent crossovers in DFA scaling, resulting from the interplay between noise and trend scaling.
• Crossover positions exhibit power-law scaling with trend parameters.
• DFA results for uncorrelated noise and trend can be predicted by superposition.
• Deviations from superposition indicate noise-trend dependence, affecting correlation properties.

Conclusions:

• Trends significantly alter DFA outcomes, creating misleading crossovers.
• Crossovers may not always signify changes in underlying signal dynamics.
• The study offers practical guidance for applying DFA to trended signals and interpreting results.
• Proper DFA application can distinguish true dynamical transitions from trend artifacts.