Assessment of long-range correlation in time series: how to avoid pitfalls

Area of Science:

• Time series analysis
• Statistical modeling
• Signal processing

Background:

• Long-range correlation is prevalent in science and engineering, yet its analysis faces unresolved issues.
• Existing methods for assessing long-range correlation lack consistent results and clear interpretation for finite data.
• Distinguishing between stationary noise and random walk processes in time series is challenging and impacts analysis.

Purpose of the Study:

• To investigate the consistency of methods for assessing long-range correlation.
• To relate fractal scaling breaks in finite time series to data parameters.
• To understand the implications of misclassifying time series as noise versus random walk processes.

Main Methods:

• Examination of three model systems: autoregressive process of order 1, on-off intermittency, and Lévy motions.
• Analysis of an engineering problem: target detection in sea-clutter radar returns.
• Development of rules of thumb for interpreting time series with long-range correlation.

Main Results:

• Insights into the circumstances affecting the consistency of long-range correlation assessment methods.
• Methods for connecting fractal scaling breaks to key data parameters in finite time series.
• Understanding of penalties associated with misinterpreting data as noise or random walk.

Conclusions:

• The study provides practical guidance for accurate analysis of time series with long-range correlation.
• Findings are relevant to pattern recognition and signal processing applications.
• Offers rules of thumb to mitigate misinterpretations in time series analysis.