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An Updated Literature Review of Distance Correlation and Its Applications to Time Series

Author

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  • Dominic Edelmann
  • Konstantinos Fokianos
  • Maria Pitsillou

Abstract

The concept of distance covariance/correlation was introduced recently to characterise dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function, and we demonstrate its applicability to time series analysis. We will see that the auto‐distance covariance/correlation function is able to identify non‐linear relationships and can be employed for testing the i.i.d. hypothesis. Comparisons with other measures of dependence are included.

Suggested Citation

  • Dominic Edelmann & Konstantinos Fokianos & Maria Pitsillou, 2019. "An Updated Literature Review of Distance Correlation and Its Applications to Time Series," International Statistical Review, International Statistical Institute, vol. 87(2), pages 237-262, August.
    • Handle: RePEc:bla:istatr:v:87:y:2019:i:2:p:237-262
    DOI: 10.1111/insr.12294
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    Cited by:

    1. Kacoutchy Jean Ayikpa & Diarra Mamadou & Pierre Gouton & Kablan Jérôme Adou, 2023. "Classification of Cocoa Pod Maturity Using Similarity Tools on an Image Database: Comparison of Feature Extractors and Color Spaces," Data, MDPI, vol. 8(6), pages 1-24, May.
    2. Dominic Edelmann & Thomas Welchowski & Axel Benner, 2022. "A consistent version of distance covariance for right‐censored survival data and its application in hypothesis testing," Biometrics, The International Biometric Society, vol. 78(3), pages 867-879, September.
    3. Emmanuel Selorm Tsyawo, 2023. "Feasible IV regression without excluded instruments," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 235-256.
    4. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Marc Hallin & Simos Meintanis & Klaus Nordhausen, 2024. "Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models," Working Papers ECARES 2024-04, ULB -- Universite Libre de Bruxelles.
    6. Gizem Hayrullahoğlu & Çiğdem Varol, 2022. "Understanding mobility dynamics using urban functions during the COVID-19 pandemic: comparison of pre-and post-new normal eras," Asia-Pacific Journal of Regional Science, Springer, vol. 6(3), pages 1087-1109, October.
    7. Dominic Edelmann & Tobias Terzer & Donald Richards, 2021. "A Basic Treatment of the Distance Covariance," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 12-25, May.
    8. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.

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