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In this paper, we propose a nonparametric statistical tool to identify the most relevant lag in the model description of a time series. It is also shown that it can be used for model identification. The statistic is based on the number of runs, when the time series is symbolized depending on the empirical quantiles of the time series. With a Monte Carlo simulation, we show the size and power performance of our new test statistic under linear and nonlinear data generating processes. From the theoretical point of view, it is the first time that symbolic analysis and runs are proposed to identifying characteristic lags and also to help in the identification of univariate time series models. From a more applied point of view, the results show the power and competitiveness of the proposed tool with respect to other techniques without presuming or specifying a model. [ABSTRACT FROM AUTHOR]

This Special Issue (SI) brings together contributions from researchers working in symbolic analysis, complex dynamics, and information theory, from both theoretical and applied perspectives. References 1 Bandt C. Entropy Ratio and Entropy Concentration Coefficient, with Application to the COVID-19 Pandemic. C. Bandt [[1]] puts forward an entropy-based concentration coefficient C that avoids the limitations of other classical concentration measures such as Gini's index. [Extracted from the article]

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test. [ABSTRACT FROM AUTHOR]

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ ∗ and embedding dimension p for phase space reconstruction. The value of τ ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τ w = (p − 1) τ ∗ , which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τ w and τ ∗ . In this paper, we suggest a simple method for estimating τ ∗ and τ w based on symbolic analysis and symbolic entropy. As in the C-C method, τ ∗ is estimated as the first local optimal time delay and τ w as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes [ABSTRACT FROM AUTHOR]

Atrial fibrillation (AF) is a sustained cardiac arrhythmia associated with stroke, heart failure, and related health conditions. Though easily diagnosed upon presentation in a clinical setting, the transient and/or intermittent emergence of AF episodes present diagnostic and clinical monitoring challenges that would ideally be met with automated ambulatory monitoring and detection. Current approaches to address these needs, commonly available both in smartphone applications and dedicated technologies, combine electrocardiogram (ECG) sensors with predictive algorithms to detect AF. These methods typically require extensive preprocessing, preliminary signal analysis, and the integration of a wide and complex array of features for the detection of AF events, and are consequently vulnerable to over-fitting. In this paper, we introduce the application of symbolic recurrence quantification analysis (SRQA) for the study of ECG signals and detection of AF events, which requires minimal pre-processing and allows the construction of highly accurate predictive algorithms from relatively few features. In addition, this approach is robust against commonly-encountered signal processing challenges that are expected in ambulatory monitoring contexts, including noisy and non-stationary data. We demonstrate the application of this method to yield a highly accurate predictive algorithm, which at optimal threshold values is 97.9% sensitive, 97.6% specific, and 97.7% accurate in classifying AF signals. To confirm the robust generalizability of this approach, we further evaluated its performance in the implementation of a 10-fold cross-validation paradigm, yielding 97.4% accuracy. In sum, these findings emphasize the robust utility of SRQA for the analysis of ECG signals and detection of AF. To the best of our knowledge, the proposed model is the first to incorporate symbolic analysis for AF beat detection. [ABSTRACT FROM AUTHOR]

This paper proposes two new nonparametric tests for independence between time series. Both tests are based on symbolic analysis, specifically on symbolic correlation integral, in order to be robust to potential unknown nonlinearities. The first test is developed for a scenario in which each considered time series is independent and therefore the interest is to ascertain if two internally independent time series share a relationship of an unknown form. This is especially relevant as the test is nuisance parameter free, as proved in the paper. The second proposed statistic tests for independence among variables, allowing these time series to exhibit within-dependence. Monte Carlo experiments are conducted to show the empirical properties of the tests. [ABSTRACT FROM AUTHOR]