title: Compounding approach for univariate time series with nonstationary variances.
abstract: A defining feature of nonstationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent variances. To model the long-term statistical behavior, we compound the local distribution with the distribution of its parameters. Here, we consider two concrete, but diverse, examples of such nonstationary systems: the turbulent air flow of a fan and a time series of foreign exchange rates. Our main focus is to empirically determine the appropriate parameter distribution for the compounding approach. To this end, we extract the relevant time scales by decomposing the time signals into windows and determine the distribution function of the thus obtained local variances.
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, Germany.
authors.forename: Rudi
authors.initials: R
authors.lastname: Schäfer
authors.affiliation: Applied Physics, University of Paderborn, Warburger Strasse 100, 33098 Paderborn, Germany and Fachbereich Physik, Philipps-Universität Marburg, Germany.
authors.forename: Sonja
authors.initials: S
authors.lastname: Barkhofen
authors.affiliation: Fakultät für Physik, Universität Duisburg-Essen, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Guhr
authors.affiliation: Fachbereich Physik, Philipps-Universität Marburg, Germany.
authors.forename: Hans-Jürgen
authors.initials: HJ
authors.lastname: Stöckmann
authors.affiliation: Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université de Nice Sophia-Antipolis, F-06108 Nice, France and Fachbereich Physik, Philipps-Universität Marburg, Germany.
authors.forename: Ulrich
authors.initials: U
authors.lastname: Kuhl