Detrending Moving Average Algorithm: Frequency Response and Scaling Performances

TL;DR

This paper analyzes the frequency response and scaling performance of the centered Detrending Moving Average (DMA) algorithm, including higher-order variants, using analytical methods and numerical validation.

Contribution

It provides a comprehensive analytical study of the scaling behavior and frequency response of higher-order DMA algorithms, extending understanding of their capabilities.

Findings

Characterizes the frequency response of higher-order DMA

Identifies the upper limit of detectable scaling exponents

Validates analytical results with numerical tests

Abstract

The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or high-dimensional arrays) either over time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent and finite scale range behavior will be discussed.