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Symbolic correlation integral

Author

Listed:
  • M. Victoria Caballero-Pintado
  • Mariano Matilla-García
  • Manuel Ruiz Marín

Abstract

This paper aims to introduce the concept of symbolic correlation integral SC that is extensively used in many scientific fields. The new correlation integral SC avoids the noisy parameter 𝜀 of the classical correlation integral, defined by Grassberger and Procaccia (1983) and extensively used for constructing correlation-integral-based statistics, as in the BDS test. Once the free parameter 𝜀 disappears, it is possible to construct a nonparametric powerful test for independence that can also be used as a diagnostic tool for model selection. The symbolic correlation integral is also extended to deal with multivariate models, and a test for causality is proposed as an example of the theoretical power of the new concept. With extensive Monte Carlo simulations, the paper shows the good size and power performance of symbolic correlation-integral-based tests.

Suggested Citation

  • M. Victoria Caballero-Pintado & Mariano Matilla-García & Manuel Ruiz Marín, 2019. "Symbolic correlation integral," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 533-556, May.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:5:p:533-556
    DOI: 10.1080/07474938.2017.1365431
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    Cited by:

    1. Fernando López & Mariano Matilla-García & Jesús Mur & Manuel Ruiz Marín, 2021. "Statistical Tests of Symbolic Dynamics," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    2. Weiß, Christian H. & Ruiz Marín, Manuel & Keller, Karsten & Matilla-García, Mariano, 2022. "Non-parametric analysis of serial dependence in time series using ordinal patterns," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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