Journal ArticleDOI
Time-reversibility of linear stochastic processes
TLDR
For discrete mixed autoregressive moving-average processes, it was shown in this paper that time reversal is a unique property of Gaussian processes, and that it is a special case of the time reversal property of discrete mixed auto-regression processes.Abstract:
Time-reversibility is defined for a process X(t) as the property that {X(t), - - -, X(t.)} and {X(- t), - -, X(- t.)} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes. TIME-REVERSIBILITY; SHOT NOISE; CHARACTERISATIONS OF THE NORMAL DISTRIBUTION; TIME SERIES; STOCHASTIC PROCESSESread more
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A review of symbolic analysis of experimental data
TL;DR: This review covers the group of data-analysis techniques collectively referred to as symbolization or symbolic time-series analysis, and indicates that symbolization can increase the efficiency of finding and quantifying information from such systems, reduce sensitivity to measurement noise, and discriminate both specific and general classes of proposed models.
Journal ArticleDOI
Some simple models for discrete variate time series
TL;DR: In this paper, simple models are presented for use in the modeling and generation of sequences of dependent discrete random variables, which are essentially Markov Chains, but are structurally autoregressions, and so depend on only a few parameters.
Journal ArticleDOI
Complex network approaches to nonlinear time series analysis
Yong Zou,Reik V. Donner,Norbert Marwan,Jonathan F. Donges,Jonathan F. Donges,Jürgen Kurths,Jürgen Kurths,Jürgen Kurths +7 more
TL;DR: An in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments, and emphasizes which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis.
Journal ArticleDOI
Some arma models for dependent sequences of Poisson counts
TL;DR: In this article, a family of models for discrete-time processes with Poisson marginal distributions is developed and investigated, and the joint distribution of n consecutive observations in a process is derived and its properties discussed.
Journal ArticleDOI
Multiscale Analysis of Heart Rate Dynamics: Entropy and Time Irreversibility Measures
TL;DR: Two recently developed multiscale computational tools are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Characterisation of the distribution of random variables in linear structural relations
TL;DR: In this paper, the authors examined the nature of the latent random variables which occur in linear structural models, under the assumption that they are independent and showed that alternative representations with different sets of coefficients for the latent variables or different numbers of latent variables are possible when and only when some of the variables or some of their linear combinations have a univariate normal distribution.