Comparison of detrending methods for fluctuation analysis

TL;DR

This paper compares different detrending methods for fluctuation analysis, finding that CMA performs similarly to DFA in certain conditions, but DFA remains preferable when the trend form is unknown.

Contribution

The study provides a detailed comparison of DFA, CMA, and MDFA, highlighting their relative performances and limitations in detecting long-range correlations.

Findings

CMA performs as well as DFA in long data with weak trends.

CMA is slightly better than DFA in short data with weak trends.

DFA generally performs better than MDFA across studied examples.

Abstract

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA is performing equivalently as DFA in long data with weak trends and slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect the different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.