Ordinal symbolic network methodologies for nonlinear time series analysis

Konstantinos Sakellariou

Research output: ThesisDoctoral Thesis

87 Downloads (Pure)

Abstract

Analysing nonlinear interactions and chaotic dynamics is essential for the study of complex systems. This thesis investigates
network-based techniques founded on the symbolic dynamics of ordinal patterns, i.s. a specific encoding of order relations
between successive measurements In a time series. Findings show that our proposed Mancovlan framework based on an
ordinal partition of state space can extract meaningful information purely from scalar projections of mixing multidimensional systems. By employing ergodic-theoretic tools, we show that such stochastic approximations to deterministic dynamics yield accurate estimates for topological and metric dynamical invariants in both discrete- and continuous-time systems.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • The University of Western Australia
Supervisors/Advisors
  • Small, Michael, Supervisor
  • Judd, Kevin, Supervisor
Award date4 Jan 2018
DOIs
Publication statusUnpublished - 2018

Fingerprint

time series analysis
methodology
theses
complex systems
partitions
coding
projection
scalars
estimates
approximation
interactions

Cite this

@phdthesis{36722aa6b8f44bb78dd8cb9de88f39eb,
title = "Ordinal symbolic network methodologies for nonlinear time series analysis",
abstract = "Analysing nonlinear interactions and chaotic dynamics is essential for the study of complex systems. This thesis investigatesnetwork-based techniques founded on the symbolic dynamics of ordinal patterns, i.s. a specific encoding of order relationsbetween successive measurements In a time series. Findings show that our proposed Mancovlan framework based on anordinal partition of state space can extract meaningful information purely from scalar projections of mixing multidimensional systems. By employing ergodic-theoretic tools, we show that such stochastic approximations to deterministic dynamics yield accurate estimates for topological and metric dynamical invariants in both discrete- and continuous-time systems.",
keywords = "nonlinear dynamics, dynamical systems, time series analysis, complex networks, Markov modelling, Ergodic theory, Ordinal patterns, Ordinal networks",
author = "Konstantinos Sakellariou",
year = "2018",
doi = "10.4225/23/5a7bb37f40b60",
language = "English",
school = "The University of Western Australia",

}

Sakellariou, K 2018, 'Ordinal symbolic network methodologies for nonlinear time series analysis', Doctor of Philosophy, The University of Western Australia. https://doi.org/10.4225/23/5a7bb37f40b60

Ordinal symbolic network methodologies for nonlinear time series analysis. / Sakellariou, Konstantinos.

2018.

Research output: ThesisDoctoral Thesis

TY - THES

T1 - Ordinal symbolic network methodologies for nonlinear time series analysis

AU - Sakellariou, Konstantinos

PY - 2018

Y1 - 2018

N2 - Analysing nonlinear interactions and chaotic dynamics is essential for the study of complex systems. This thesis investigatesnetwork-based techniques founded on the symbolic dynamics of ordinal patterns, i.s. a specific encoding of order relationsbetween successive measurements In a time series. Findings show that our proposed Mancovlan framework based on anordinal partition of state space can extract meaningful information purely from scalar projections of mixing multidimensional systems. By employing ergodic-theoretic tools, we show that such stochastic approximations to deterministic dynamics yield accurate estimates for topological and metric dynamical invariants in both discrete- and continuous-time systems.

AB - Analysing nonlinear interactions and chaotic dynamics is essential for the study of complex systems. This thesis investigatesnetwork-based techniques founded on the symbolic dynamics of ordinal patterns, i.s. a specific encoding of order relationsbetween successive measurements In a time series. Findings show that our proposed Mancovlan framework based on anordinal partition of state space can extract meaningful information purely from scalar projections of mixing multidimensional systems. By employing ergodic-theoretic tools, we show that such stochastic approximations to deterministic dynamics yield accurate estimates for topological and metric dynamical invariants in both discrete- and continuous-time systems.

KW - nonlinear dynamics

KW - dynamical systems

KW - time series analysis

KW - complex networks

KW - Markov modelling

KW - Ergodic theory

KW - Ordinal patterns

KW - Ordinal networks

U2 - 10.4225/23/5a7bb37f40b60

DO - 10.4225/23/5a7bb37f40b60

M3 - Doctoral Thesis

ER -