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Compounding approach for univariate time series with non-stationary variances

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  • Rudi Schafer
  • Sonja Barkhofen
  • Thomas Guhr
  • Hans-Jurgen Stockmann
  • Ulrich Kuhl

Abstract

A defining feature of non-stationary 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 parameters. 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 non-stationary 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 have to estimate the parameter distribution for univariate time series in a highly non-stationary situation.

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  • Rudi Schafer & Sonja Barkhofen & Thomas Guhr & Hans-Jurgen Stockmann & Ulrich Kuhl, 2015. "Compounding approach for univariate time series with non-stationary variances," Papers 1503.02177, arXiv.org.
    • Handle: RePEc:arx:papers:1503.02177
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    File URL: http://arxiv.org/pdf/1503.02177
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    Cited by:

    1. Thomas Guhr & Andreas Schell, 2020. "Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations," Papers 2011.07570, arXiv.org.

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