Statistical Analysis of Time Series

Statistical analysis of time series is still inadequate within circulation research. With the advent of increasing computational power and real-time recordings from hemodynamic studies, one is increasingly dealing with vast amounts of data in time series. This paper aims to illustrate how statistical analysis using the significant nonstationarities (SiNoS) method may complement traditional repeated-measures ANOVA and linear mixed models. We applied these methods on a dataset of local hepatic and systemic circulatory changes induced by aortoportal shunting and graded liver resection. We found SiNoS analysis more comprehensive when compared with traditional statistical analysis in the following four ways: 1) the method allows better signal-to-noise detection; 2) including all data points from real time recordings in a statistical analysis permits better detection of significant features in the data; 3) analysis with multiple scales of resolution facilitates a more differentiated observation of the material; and 4) the method affords excellent visual presentation by combining group differences, time trends, and multiscale statistical analysis allowing the observer to quickly view and evaluate the material. It is our opinion that SiNoS analysis of time series is a very powerful statistical tool that may be used to complement conventional statistical methods.

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Chaotic Evolution and Strange Attractors: The Statistical Analysis of Time Series for Deterministic Nonlinear Systems (David Ruelle)

SIAM Review ◽

10.1137/1033084 ◽

1991 ◽

Vol 33 (2) ◽

pp. 328-329

Author(s):

R. S. MacKay

Keyword(s):

Time Series ◽

Statistical Analysis ◽

Nonlinear Systems ◽

Strange Attractors ◽

Analysis Of Time Series

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Case IV Statistical Analysis of VEP and AI by the Principal Component Analysis of Time Series in Frequency Domain

Case Studies in Time Series Analysis ◽

10.1142/9789812796516_0007 ◽

1993 ◽

pp. 162-177

Keyword(s):

Principal Component Analysis ◽

Time Series ◽

Statistical Analysis ◽

Frequency Domain ◽

Principal Component ◽

Component Analysis ◽

Analysis Of Time Series

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CHAOS IN HETEROGENEOUS NETWORKS WITH TEMPORALLY INERT NODES

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409023032 ◽

2009 ◽

Vol 19 (02) ◽

pp. 677-686

Author(s):

J. J. TORRES ◽

J. MARRO ◽

S. DE FRANCISCIS

Keyword(s):

Neural Network ◽

Time Series ◽

Statistical Analysis ◽

Power Law ◽

Heterogeneous Networks ◽

Heterogeneous Distribution ◽

Dynamic Attractors ◽

Short Time ◽

Degree Of Order ◽

Analysis Of Time Series

We discuss an attractor neural network in which only a fraction ρ of nodes is simultaneously updated. In addition, the network has a heterogeneous distribution of connection weights and, depending on the current degree of order, connections are changed at random by a factor Φ on short-time scales. The resulting dynamic attractors may become unstable in a certain range of Φ thus ensuing chaotic itineracy which highly depends on ρ. For intermediate values of ρ, we observe that the number of attractors visited increases with ρ, and that the trajectory may change from regular to chaotic and vice versa as ρ is modified. Statistical analysis of time series shows a power-law spectra under conditions in which the attractors' space is most efficiently explored.

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