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Detrending moving average algorithm: Frequency response and scaling performances.

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  • 1Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Physical Review. E
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The Detrending Moving Average (DMA) algorithm analyzes long-range correlations in random data. This study explores higher-order DMA scaling performance using analytical and numerical methods for better signal characterization.

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Area of Science:

  • Signal Processing
  • Statistical Analysis
  • Time Series Analysis

Background:

  • The Detrending Moving Average (DMA) algorithm is a key tool for analyzing long-range correlations in random signals and datasets.
  • Various DMA algorithm variants are employed across time and space for characterizing sequences and arrays.

Purpose of the Study:

  • To investigate the scaling performance of centered Detrending Moving Average (DMA) algorithms, including higher-order variants.
  • To analyze DMA performance using analytical arguments, continuous time approximation, and frequency response methods.

Main Methods:

  • Analytical arguments and continuous time approximation to model DMA behavior.
  • Frequency response approach to assess scaling characteristics.
  • Numerical tests to validate analytical findings for higher-order DMA.

Main Results:

  • Detailed analysis of detrending power degree and frequency response for higher-order DMA.
  • Characterization of asymptotic scaling and the upper limit of detectable scaling exponents.
  • Investigation of finite scale range behavior in DMA performance.

Conclusions:

  • The study provides a comprehensive understanding of higher-order DMA scaling performance.
  • Results are validated through analytical derivations and numerical simulations.
  • The findings enhance the application of DMA for accurate signal and data analysis.