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Detection of a long-range correlation with an adaptive detrending method.

Chang-Yong Lee¹

¹Department of Industrial and Systems Engineering, Kongju National University, Kongju 314-701, South Korea. clee@kongju.ac.kr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This study introduces a new regression analysis method to accurately estimate scaling exponents in nonstationary time series. The approach effectively removes trends, preventing artificial crossovers for reliable long-range correlation analysis.

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Area of Science:

Time Series Analysis
Statistical Physics
Signal Processing

Background:

Nonstationary time series exhibit trends that complicate the analysis of long-range correlations.
Traditional methods for estimating scaling exponents can introduce artificial crossovers due to unremoved trends.
Accurate estimation of scaling exponents is crucial in various fields, including physics and finance.

Purpose of the Study:

To propose a novel methodology for estimating scaling exponents in nonstationary time series using regression analysis.
To develop a technique that adaptively removes trends, thereby avoiding artificial crossovers in scaling exponent estimation.
To validate the proposed methodology by applying it to detrended fluctuation analysis.

Main Methods:

A regression analysis approach with adaptive degree determination of the regression polynomial.
Application of the methodology to detrended fluctuation analysis (DFA).
Testing with correlated data containing various superimposed trends.

Main Results:

The proposed methodology successfully removes various types of trends embedded in nonstationary signals.
Artificial crossovers, often seen in conventional techniques, were eliminated.
The method demonstrated validity in estimating scaling exponents without introducing artifacts.

Conclusions:

The developed methodology provides a robust way to estimate scaling exponents in nonstationary time series.
Adaptive trend removal is key to overcoming limitations of conventional methods.
The approach offers improved statistical characteristics for scaling exponent estimation.