scholarly journals A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots

Vibration ◽  
2019 ◽  
Vol 2 (4) ◽  
pp. 332-368 ◽  
Author(s):  
Bedartha Goswami
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Nonlinear Time Series ◽  
Recurrence Plot ◽  
Series Data ◽  
Nonlinear Time Series Analysis ◽  
Recurrence Plots ◽  
Series Analysis ◽  
Wide Range ◽  
Dynamical Features

Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated.

Why Study Nonlinear Time Series Analysis?

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
System Dynamics ◽  
Real World ◽  
Time Series Data ◽  
Nonlinear Time Series ◽  
Series Data ◽  
Nonlinear Time Series Analysis ◽  
Deterministic System ◽  
Series Analysis

Nonlinear Time Series Analysis (NLTS) provides a mathematically rigorous collection of techniques designed to reconstruct real-world system dynamics from time series data on a single variable or multiple causally-related variables. NLTS facilitates scientific inquiry that emphasizes strong supportive evidence, well-conducted and thorough inquiry, and realism. Data provide an essential evidentiary portal to a reality to which we have only limited access. Random-appearing data do not prove that underlying dynamic process are subject to exogenous inherently-random forces. The possibility exists that observed volatility is generated by inherently-unstable, deterministic, and nonlinear real-world dynamic systems. NLTS allows the data to speak regarding which type of system dynamics generated them. It is capable of detecting linear as well as nonlinear deterministic system dynamics, and diagnosing the presence of linear stochastic dynamics. Our objective is to use NLTS to uncover the structure best corresponding to reality whether it be linear, nonlinear, deterministic, or stochastic. Accurate diagnosis of real-world dynamics from observed data is crucial to develop valid theory, and to formulate effective public policy based on theory.

Nonlinear Time Series Analysis with R

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Particle Physics ◽  
Linear Time ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Series Analysis ◽  
Linear Behavior ◽  
Non Linear ◽  
Scientific Principles

In the process of data analysis, the investigator is often facing highly-volatile and random-appearing observed data. A vast body of literature shows that the assumption of underlying stochastic processes was not necessarily representing the nature of the processes under investigation and, when other tools were used, deterministic features emerged. Non Linear Time Series Analysis (NLTS) allows researchers to test whether observed volatility conceals systematic non linear behavior, and to rigorously characterize governing dynamics. Behavioral patterns detected by non linear time series analysis, along with scientific principles and other expert information, guide the specification of mechanistic models that serve to explain real-world behavior rather than merely reproducing it. Often there is a misconception regarding the complexity of the level of mathematics needed to understand and utilize the tools of NLTS (for instance Chaos theory). However, mathematics used in NLTS is much simpler than many other subjects of science, such as mathematical topology, relativity or particle physics. For this reason, the tools of NLTS have been confined and utilized mostly in the fields of mathematics and physics. However, many natural phenomena investigated I many fields have been revealing deterministic non linear structures. In this book we aim at presenting the theory and the empirical of NLTS to a broader audience, to make this very powerful area of science available to many scientific areas. This book targets students and professionals in physics, engineering, biology, agriculture, economy and social sciences as a textbook in Nonlinear Time Series Analysis (NLTS) using the R computer language.

NONLINEAR TIME SERIES ANALYSIS OF ELECTROENCEPHALOGRAM TRACINGS OF CHILDREN WITH AUTISM

2012 ◽  
Vol 22 (03) ◽  
pp. 1250044
Author(s):  
LANCE ONG-SIONG CO TING KEH ◽  
ANA MARIA AQUINO CHUPUNGCO ◽  
JOSE PERICO ESGUERRA
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Prediction Error ◽  
Children With Autism ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Normal Children ◽  
Series Analysis ◽  
Significant Difference ◽  
Severe Autism

Three methods of nonlinear time series analysis, Lempel–Ziv complexity, prediction error and covariance complexity were employed to distinguish between the electroencephalograms (EEGs) of normal children, children with mild autism, and children with severe autism. Five EEG tracings per cluster of children aged three to seven medically diagnosed with mild, severe and no autism were used in the analysis. A general trend seen was that the EEGs of children with mild autism were significantly different from those with severe or no autism. No significant difference was observed between normal children and children with severe autism. Among the three methods used, the method that was best able to distinguish between EEG tracings of children with mild and severe autism was found to be the prediction error, with a t-Test confidence level of above 98%.

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