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Detrended fluctuation analysis as a regression framework: Estimating dependence at different scales

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  • Ladislav Kristoufek

Abstract

We propose a framework combining detrended fluctuation analysis with standard regression methodology. The method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential non-stationarity and power-law correlations. The former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives. The latter ones make the method a significant improvement over the standard least squares estimation. Theoretical claims are supported by Monte Carlo simulations. The method is then applied on selected examples from physics, finance, environmental science and epidemiology. For most of the studied cases, the relationship between variables of interest varies strongly across scales.

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  • Ladislav Kristoufek, 2014. "Detrended fluctuation analysis as a regression framework: Estimating dependence at different scales," Papers 1411.0496, arXiv.org, revised Jan 2015.
    • Handle: RePEc:arx:papers:1411.0496
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    Cited by:

    1. Paulo Ferreira, 2017. "Portuguese and Brazilian stock market integration: a non-linear and detrended approach," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 16(1), pages 49-63, April.
    2. Ladislav Kristoufek, 2016. "Power-law cross-correlations estimation under heavy tails," Papers 1602.05385, arXiv.org, revised Apr 2016.
    3. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.

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