scholarly journals Spectral analysis of sample autocovariance matrices of a class of linear time series in moderately high dimensions

Bernoulli ◽  
2017 ◽  
Vol 23 (4A) ◽  
pp. 2181-2209 ◽  
Author(s):  
Lili Wang ◽  
Alexander Aue ◽  
Debashis Paul
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Linear Time ◽  
High Dimensions ◽  
Autocovariance Matrices ◽  
Sample Autocovariance

scholarly journals Correlating the non-linear time series and spectral properties of IGR J17091–3624: is it similar to GRS 1915+105?

2020 ◽  
Vol 492 (3) ◽  
pp. 4033-4042
Author(s):  
Oluwashina Adegoke ◽  
Banibrata Mukhopadhyay ◽  
Ranjeev Misra
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Integral Method ◽  
Spectral Properties ◽  
Linear Time ◽  
Poisson Noise ◽  
Accretion Discs ◽  
Correlation Integral ◽  
Non Linear ◽  
Time Series Analyses

ABSTRACT Using the correlation integral method, we explore the non-linear properties of IGR J17091–3624 by comparing the underlying behaviour to GRS 1915+105. We find that while GRS 1915+105 is known to reveal a combination of fractal (or even chaotic) and stochastic behaviours depending on its temporal class, IGR J17091–3624 mostly shows stochastic behaviour. Therefore, although several observations find that IGR J17091–3624 is similar to GRS 1915+105, and that they have temporal classes in common, the underlying non-linear time series analyses offer a different view. Nevertheless, the ratio of the Poisson noise to rms variation for IGR J17091–3624 turns out to be high, suggesting that it is dominated by Poisson noise. Hence it might plausibly lead to the suppression of its non-linear properties, if there is any. Indeed, IGR J17091–3624 is a very faint source compared with GRS 1915+105. However, by increasing the time bin, some of the temporal classes of IGR J17091–3624 show deviation from stochasticity, indicating the plausibility of a higher fractal dimension. Along with spectral analysis, overall IGR J17091–3624 seems to reveal three different accretion classes: slim, Keplerian and advective accretion discs.

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.

scholarly journals Hybrid forecasting model for non-linear time series

2020 ◽  
Author(s):  
E. Priyadarshini ◽  
G. Raj Gayathri ◽  
M. Vidhya ◽  
A. Govindarajan ◽  
Samuel Chakkravarthi
Keyword(s):  
Time Series ◽  
Linear Time ◽  
Forecasting Model ◽  
Non Linear ◽  
Hybrid Forecasting
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