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>