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Multivariate rescaled range analysis

Author

Listed:
  • Meraz, M.
  • Alvarez-Ramirez, J.
  • Rodriguez, E.

Abstract

The rescaled range analysis introduced by H.E. Hurst in 1951 has been a useful tool for the analysis of complex univariate signals. However, in many instances one dispose of multichannel signals, for which a rescaled range analysis is required. This work aims to propose a straightforward extension to the multivariate case which resembles the computations steps of the univariate case. Two worked examples were used to illustrate the computations. The first example is the Dow Jones financial market comprising the index and trading volume. The second instance corresponds to the seismic activity in Southern Mexico (2019–2021), which considered four recorded variables (seismic magnitude, latitude, longitude, and depth). These results showed that the multivariate rescaled range analysis of complex systems improves the understanding of these systems relative to studies made with univariate rescaled range analysis.

Suggested Citation

  • Meraz, M. & Alvarez-Ramirez, J. & Rodriguez, E., 2022. "Multivariate rescaled range analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    • Handle: RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121008815
    DOI: 10.1016/j.physa.2021.126631
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    1. Meraz, Monica & Carbó, Roxana & Rodriguez, Eduardo & Alvarez-Ramirez, Jose, 2023. "Fractal correlations in the Covid-19 genome sequence via multivariate rescaled range analysis," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Marin-Lopez, A. & Martínez-Cadena, J.A. & Martinez-Martinez, F. & Alvarez-Ramirez, J., 2023. "Surrogate multivariate Hurst exponent analysis of gait dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Vogl, Markus, 2023. "Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framewo," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).

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