Detection and characterization of changes of the correlation structure in multivariate time series

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Markus Müller ◽  
Gerold Baier ◽  
Andreas Galka ◽  
Ulrich Stephani ◽  
Hiltrud Muhle
1982 ◽  
Vol 19 (2) ◽  
pp. 463-468 ◽  
Author(s):  
Ed Mckenzie

A non-linear stationary stochastic process {Xt} is derived and shown to have the property that both the processes {Xt} and {log Xt} have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obtained.


1982 ◽  
Vol 19 (02) ◽  
pp. 463-468 ◽  
Author(s):  
Ed Mckenzie

A non-linear stationary stochastic process {Xt } is derived and shown to have the property that both the processes {Xt } and {log Xt } have the same correlation structure, viz. the Markov or first-order autoregressive correlation structure. The generation of such processes is discussed briefly and a characterization of the gamma distribution is obtained.


2017 ◽  
Vol 1 (3) ◽  
pp. 208-221 ◽  
Author(s):  
Speranza Sannino ◽  
Sebastiano Stramaglia ◽  
Lucas Lacasa ◽  
Daniele Marinazzo

Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool, and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (a) this approach allows vs to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (b) this provides a suggestive bridge between time series and network theory that nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting-state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach.


2017 ◽  
Author(s):  
Speranza Sannino ◽  
Sebastiano Stramaglia ◽  
Lucas Lacasa ◽  
Daniele Marinazzo

AbstractVisibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (i) this approach allows to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (ii) this provides a suggestive bridge between time series and network theory which nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach.


Sign in / Sign up

Export Citation Format

Share Document