Assessing Serial Dependence in Ordinal Patterns Processes Using Chi-squared Tests with Application to EEG Data Analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F22%3A00560397" target="_blank" >RIV/67985807:_____/22:00560397 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00023752:_____/22:43920917

Výsledek na webu

<a href="https://dx.doi.org/10.1063/5.0096954" target="_blank" >https://dx.doi.org/10.1063/5.0096954</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0096954" target="_blank" >10.1063/5.0096954</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Assessing Serial Dependence in Ordinal Patterns Processes Using Chi-squared Tests with Application to EEG Data Analysis

Popis výsledku v původním jazyce

We extend Elsinger’s work on chi-squared tests for independence using ordinal patterns and investigate the general class of m-dependent ordinal patterns processes, to which belong ordinal patterns processes derived from random walk, white noise, and moving average processes. We describe chi-squared asymptotically distributed statistics for such processes that take into account necessary constraints on ordinal patterns probabilities and propose a test for m-dependence, with which we are able to quantify the range of serial dependence in a process. We apply the test to epilepsy electroencephalography time series data and observe shorter m-dependence associated with seizures, suggesting that the range of serial dependence decreases during those events. The ordinal patterns symbolization transforms a real-valued time series into a sequence of symbols called ordinal patterns, which simplifies statistical analysis while keeping information about up and down movements. Despite the increasing interest in its application due to the need to understand complex nonlinear dynamics based on observed time series, analytical properties of the distributions of ordinal patterns frequencies are not yet fully known. By modeling a sequence of ordinal patterns as the output of a symbolic process, we study m-dependent ordinal patterns processes, i.e., symbolic processes in the space of ordinal patterns whose maximum dependence range is m. We derive chi-squared asymptotically distributed statistics for this class of processes and use them to evaluate the range of serial dependence in general ordinal patterns processes. Applying the results to analyze epilepsy electroencephalography (EEG) time series, we find that seizure events are characterized by a decrease in the range of serial dependence of the ordinal dynamics.

Název v anglickém jazyce

Assessing Serial Dependence in Ordinal Patterns Processes Using Chi-squared Tests with Application to EEG Data Analysis

Popis výsledku anglicky

We extend Elsinger’s work on chi-squared tests for independence using ordinal patterns and investigate the general class of m-dependent ordinal patterns processes, to which belong ordinal patterns processes derived from random walk, white noise, and moving average processes. We describe chi-squared asymptotically distributed statistics for such processes that take into account necessary constraints on ordinal patterns probabilities and propose a test for m-dependence, with which we are able to quantify the range of serial dependence in a process. We apply the test to epilepsy electroencephalography time series data and observe shorter m-dependence associated with seizures, suggesting that the range of serial dependence decreases during those events. The ordinal patterns symbolization transforms a real-valued time series into a sequence of symbols called ordinal patterns, which simplifies statistical analysis while keeping information about up and down movements. Despite the increasing interest in its application due to the need to understand complex nonlinear dynamics based on observed time series, analytical properties of the distributions of ordinal patterns frequencies are not yet fully known. By modeling a sequence of ordinal patterns as the output of a symbolic process, we study m-dependent ordinal patterns processes, i.e., symbolic processes in the space of ordinal patterns whose maximum dependence range is m. We derive chi-squared asymptotically distributed statistics for this class of processes and use them to evaluate the range of serial dependence in general ordinal patterns processes. Applying the results to analyze epilepsy electroencephalography (EEG) time series, we find that seizure events are characterized by a decrease in the range of serial dependence of the ordinal dynamics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Chaos

ISSN

1054-1500

e-ISSN

1089-7682

Svazek periodika

32

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

073126

Kód UT WoS článku

000901372800004

EID výsledku v databázi Scopus

2-s2.0-85135218899