Time-Delay Identification Using Multiscale Ordinal Quantifiers - Soriano, Miguel C.; Zunino, Luciano (Entropy, 2021)
This article belongs to the Special Issue Ordinal and Pattern-Based Quantifiers for Complex Time Series Analysis. Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon. This research was partially funded by Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina; the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017-0711) and through the QUARESC project (PID2019-109094GB-C21 and -C22/AEI/10.13039/501100011033). The work of MCS has been supported by MICINN/AEI/FEDER and the University of the Balearic Islands through a “Ramon y Cajal” Fellowship (RYC-2015-18140).