Vol. 7, No. 2, 2012

Download this article
Download this article For screen
For printing
Recent Issues
Volume 12, Issue 1
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 1
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 1
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 1
Volume 3, Issue 1
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
Subscriptions
Editorial Board
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
Analysis of persistent nonstationary time series and applications

Philipp Metzner, Lars Putzig and Illia Horenko

Vol. 7 (2012), No. 2, 175–229
Abstract

We give an alternative and unified derivation of the general framework developed in the last few years for analyzing nonstationary time series. A different approach for handling the resulting variational problem numerically is introduced. We further expand the framework by employing adaptive finite element algorithms and ideas from information theory to solve the problem of finding the most adequate model based on a maximum-entropy ansatz, thereby reducing the number of underlying probabilistic assumptions. In addition, we formulate and prove the result establishing the link between the optimal parametrizations of the direct and the inverse problems and compare the introduced algorithm to standard approaches like Gaussian mixture models, hidden Markov models, artificial neural networks and local kernel methods. Furthermore, based on the introduced general framework, we show how to create new data analysis methods for specific practical applications. We demonstrate the application of the framework to data samples from toy models as well as to real-world problems such as biomolecular dynamics, DNA sequence analysis and financial applications.

Keywords
nonstationary time series analysis, nonstationary data analysis, clustering, finite element method
Mathematical Subject Classification 2010
Primary: 60G20, 62H25, 62H30, 62M10, 62M20
Secondary: 62M07, 62M09, 62M05, 62M02
Milestones
Received: 29 July 2011
Revised: 23 March 2012
Accepted: 5 May 2012
Published: 16 October 2012
Authors
Philipp Metzner
Institute of Computational Science, Faculty of Informatics
Università della Svizzera italiana
Via Guiseppe Buffi 13
CH-6900 Lugano
Switzerland
http://icsweb.inf.unisi.ch/cms/index.php/people/24-philipp-metzner.html
Lars Putzig
Institute of Computational Science, Faculty of Informatics
Università della Svizzera italiana
Via Guiseppe Buffi 13
CH-6900 Lugano
Switzerland
http://icsweb.inf.unisi.ch/cms/index.php/people/27-lars-putzig.html
Illia Horenko
Institute of Computational Science, Faculty of Informatics
Università della Svizzera italiana
Via Guiseppe Buffi 13
CH-6900 Lugano
Switzerland
http://icsweb.inf.unisi.ch/cms/index.php/people/20-illia-horenko.html