Partial Transfer Entropy on Rank Vectors

TL;DR

This paper introduces partial transfer entropy on rank vectors (PTERV) for multivariate time series, extending existing measures to account for confounding variables and evaluating its statistical properties and performance.

Contribution

The paper extends transfer entropy on rank vectors to multivariate data with confounders, analyzing its properties and comparing its effectiveness with other measures.

Findings

PTERV outperforms PSTE in simulations.

PTERV is more robust to drifts and detrending.

Parametric tests are less powerful than surrogate-based tests.

Abstract

For the evaluation of information flow in bivariate time series, information measures have been employed, such as the transfer entropy (TE), the symbolic transfer entropy (STE), defined similarly to TE but on the ranks of the components of the reconstructed vectors, and the transfer entropy on rank vectors (TERV), similar to STE but forming the ranks for the future samples of the response system with regard to the current reconstructed vector. Here we extend TERV for multivariate time series, and account for the presence of confounding variables, called partial transfer entropy on ranks (PTERV). We investigate the asymptotic properties of PTERV, and also partial STE (PSTE), construct parametric significance tests under approximations with Gaussian and gamma null distributions, and show that the parametric tests cannot achieve the power of the randomization test using time-shifted surrogates. Using simulations on known coupled dynamical systems and applying parametric and randomization significance tests, we show that PTERV performs better than PSTE but worse than the partial transfer entropy (PTE). However, PTERV, unlike PTE, is robust to the presence of drifts in the time series and it is also not affected by the level of detrending.