On the limits of probabilistic forecasting in nonlinear time series analysis II: Differential entropy

2017 ◽  
Vol 27 (8) ◽  
pp. 083125 ◽  
Author(s):  
José M. Amigó ◽  
Yoshito Hirata ◽  
Kazuyuki Aihara
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Differential Entropy ◽  
Probabilistic Forecasting ◽  
Series Analysis

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%.

Sign in / Sign up

Export Citation Format

Share Document