Open Access
2012 Analysis of persistent nonstationary time series and applications
Philipp Metzner, Lars Putzig, Illia Horenko
Commun. Appl. Math. Comput. Sci. 7(2): 175-229 (2012). DOI: 10.2140/camcos.2012.7.175


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.


Download Citation

Philipp Metzner. Lars Putzig. Illia Horenko. "Analysis of persistent nonstationary time series and applications." Commun. Appl. Math. Comput. Sci. 7 (2) 175 - 229, 2012.


Received: 29 July 2011; Revised: 23 March 2012; Accepted: 5 May 2012; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1275.62067
MathSciNet: MR3005737
Digital Object Identifier: 10.2140/camcos.2012.7.175

Primary: 60G20 , 62H25 , 62H30 , 62M10 , 62M20
Secondary: 62M02 , 62M05 , 62M07 , 62M09

Keywords: clustering , finite element method , nonstationary data analysis , nonstationary time series analysis

Rights: Copyright © 2012 Mathematical Sciences Publishers

Vol.7 • No. 2 • 2012
Back to Top