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Statistical Analysis of Networks - Module on Time Series Networks 2018-2019

The module "Time Series Networks" constitutes part of the course "Statistical Analysis of Networks" of the postgraduate program "Web Science" organized by the Department of Mathematics of AUTh.

Instructor:
Dimitris Kugiumtzis

Content:

Syllabus, suggested literature

Syllabus:

The module is about the construction of networks from multivariate time-series, where each time-series defines the node, and the association of two time-series determines the link between the respective nodes.

 

The main objective of the module is the study of different types of association (connection / link) between two time series and the networks derived from such associations.

 

The module is divided in three parts and each part is taught at a 4-hour course (see Course transperancies).

  1. Association networks, correlation networks, cross-correlation, partial cross-correlation, parametric and non-parametric tests of significance of correlation, correlation network from time-series. Examples.

  2. Uni-variate time-series (stationarity, time series decomposition, detrending), autocorrelation and mutual information, test for independence, linear autoregressive models. Bi-variate time-series, cross-correlation and cross-mutual information. Examples.

  3. Linear stochastic and nonlinear deterministic systems. Correlation measures. Construction of correlation networks from time series. Examples.

  4. Nonlinear and nonlinear causality measures. Connectivity networks using causality measures on multivariate time series. Applications to neuroscience and finance.

  5. Networkd from time series in Matlab. Practical application of methods presented in the first four parts using the computational software Matlab.

Suggested literature:

Suggested books:

  1. J. Pearl (1998), "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", Morgan Kaufmann.

  2.  E.D. Kolaczyk (2009), "Statistical Analysis of Network Data", Springer

  3. Horvath, S. (2011) Weighted Network Analysis, Applications in Genomics and Systems Biology. New York:
    Springer

  4. Fornito, A., Bullmore, E. T. & Zalesky, A. (2016) Fundamentals of Brain Network Analysis, 1st edn.
    Cambridge, Massachusetts, United States: Academic Press, Elsevier

Suggested edited collection of papers:

  1. A. Reggiani and P. Nijkamp (2006), "Spatial Dynamics, Networks And Modelling (New Horizons in Regional Science Series)", Edward Elgar Publishing.

  2.  T. Gross and H. Sayama (2009), "Adaptive Networks: Theory, Models and Applications (Understanding Complex Systems)", Springer.

  3.  R. Menezes, S. Fortunato, G. Mangioni and V. Nicosia (2009), "Complex Networks: Results of the 1st International Workshop on Complex Networks (CompleNet 2009) (Studies in Computational Intelligence)", Springer.

  4.  N. Ganguly, A. Deutsch and A. Mukherjee (2009), "Dynamics On and Of Complex Networks: Applications to Biology, Computer Science, and the Social Sciences (Modeling and Simulation in Science, Engineering and Technology)", Birkhauser Boston.

  5. S. K. Dana, P. K. Roy, and J. Kurths, Eds., Complex Dynamics in Physiological Systems: From Heart to Brain, ser. Series: Understanding Complex Systems. Berlin / Heidelberg: Springer, 2009

To view the networks, the software pajek will be used (see http://pajek.imfm.si)

 Course transparencies

  1. Course 1: Introduction to networks, correlation and time series (in PDF) [last update 8/11/2018]
    - Introduction to association networks. Example from scientometrics.
    -     Correlation networks. Cross-correlation, parametric and non-parametric tests of significance of correlation. Partial cross-correlation and tests of significance. Example for correlation network from gene regulation of micro-array data.
    - Correlation network and time-series. Example of correlation network from world market indices.

         Data files for course 1:
    1. Ecoliv4Build6ex1.xls (excel format), Ecoliv4Build6ex1.txt (plain text format): Micro-array data.
        Source: http://m3d.bu.edu/cgi-bin/web/array/index.pl (data base Palsson03).
    2. WorldMarkets.dat (plain text format). The data are in a matrix form of size 101 x 8, containing the indices over 101 days from 8 world stock markets (USA, Australia, United Kingdom, Germany, Greece, Malaysia, South Africa, Croatia).
        Source: Morgan Stanley Capital International’s market capitalization weighted index data 
    3. WorldIndicesCorrCoeff.net (format suitable for pajek software). It contains the information of nodes (vertices) and links (arcs) of the correlation network for the 8 world markets.
    4. WorldIndicesPartCorr.net The same as for "WorldIndicesCorrCoeff.net" but for the partial correlation network.
     
  2. Course 2: Measure of correlation, complexity and coupling for time-series (in PDF) [last update 29/3/2011]
    - Time series, stationarity, time series decomposition, detrending. Examples.
    -     Autocorrelation, test for independence, linear autoregressive models. Examples.
    -     Mutual information and test for independence. Examples.
    -     Bi-variate time-series, cross-correlation and cross-mutual information. Examples.

    Data files for course 2:
    1. GPIC2001_2005residuals.dat (plain text format): The monthly General Consumer Price Index for the period Jan 2001 - Aug 2005.
    2. PacketArrival.dat (plain text format). A trace containing packet arrivals seen on an Ethernet at the Bellcore Morristown Research and Engineering facility, regarding LAN traffic, period 11:25 on August 29, 1989.
    2. USAreturns.dat (plain text format). Daily returns of the USA marker index for an unspecified period     of 300 days.
        Source: Morgan Stanley Capital International’s market capitalization weighted index data 
    3. Matlab program and functions: Exercise2.m, ARm.m, mutual.m, portmanteauLB.m.
  3. Course 3: Multivariate time series and networks (in PDF) [last update 17/3/2010]
    - Spurious cross-correlation, vector autoregressive models and dynamic regression models. Examples.
    -     Nonlinear dynamical systems, coupled dynamical systems. Examples.
    -     Correlation and causality measures and construction of networks from time series. Examples. 

  4. Course 4 : Connectivity Networks and Applications (σε PDF) 
    - Survey of measures for causality and correlation
    -     Granger causality index and conditional Granger causality index
    -     Measures of Granger causality based on information theory
    -     Evaluation of Granger causality measures on known systems (stochastic linear and nonlinear, coupled Henon maps)
    -     Application of Granger causality measures on electroencephalograms (EEG). 

  5. Course 5: Exercises on Matlab.

Exercises and computer programs

To view multiple time series in a graphical Matlab environment you may use the toolkit Measures of Time Series Analysis (MATS) that can be downloaded at http://eeganalysis.web.auth.gr (Software).

All Matlab programs for the course in a compressed file: matlab.zip.

Data files in a compressed file: Data.zip

Course examination and marking

The mark for the module "Time series networks" will be determined based on the project the students have to deliver, formed in groups of up to two students, as well as their presence and discussion at the presentation of the projects.

The project will be given at the end of the course.

The teams of one or two students should send the presentation (e.g. in PowerPoint, LaTeX) by e-mail to the teacher (dkugiu@auth.gr) not later than the last day/night before the date of "examination". The examination will take place on 13/2/2019, at 17.00, at the Math computer lab, that is there will be presentations of 8 minutew maximum followed by questions and discussions.

Updated on 8/11/2018 from Dimitris Kugiumtzis E-MAIL dkugiu@auth.gr