Repository: Freie Universit├Ąt Berlin, Math Department

Analysis of persistent non-stationary time series and applications

Metzner, Ph. and Putzig, L. and Horenko, I. (2012) Analysis of persistent non-stationary time series and applications. Communications in Applied Mathematics and Computational Science, 7 (2). pp. 175-229.

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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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:1372
Deposited By: Ulrike Eickers
Deposited On:28 Jan 2014 08:28
Last Modified:28 Jan 2014 08:28

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