10.6084/m9.figshare.5297671.v1 M. Victoria Caballero-Pintado M. Victoria Caballero-Pintado Mariano Matilla-García Mariano Matilla-García Manuel Ruiz Marín Manuel Ruiz Marín Symbolic correlation integral Taylor & Francis Group 2017 BDS statistic causality tests correlation integral independence tests symbolic dynamics C12 C14 C22 C32 C46 2017-08-10 15:23:32 Journal contribution https://tandf.figshare.com/articles/journal_contribution/Symbolic_correlation_integral/5297671 <p>This paper aims to introduce the concept of symbolic correlation integral <i>SC</i> that is extensively used in many scientific fields. The new correlation integral <i>SC</i> avoids the noisy parameter <i>𝜀</i> of the classical correlation integral, defined by Grassberger and Procaccia (<a href="#CIT0013" target="_blank">1983</a>) and extensively used for constructing correlation-integral-based statistics, as in the BDS test. Once the free parameter <i>𝜀</i> 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.</p>