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Sample Path Asymmetries in Non-Gaussian Random Processes

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Listed:
  • Anastassia Baxevani
  • Krzysztof Podgórski
  • Jörg Wegener

Abstract

type="main" xml:id="sjos12086-abs-0001"> We tackle an important although rarely addressed question of accounting for a variety of asymmetries frequently observed in stochastic temporal/spatial records. First, we review some measures intending to capture such asymmetries that have been introduced on various occasions in the past and then propose a family of measures that is motivated by Rice's formula for crossing level distributions of the slope. We utilize those asymmetry measures to demonstrate how a class of second-order models built on the skewed Laplace distributions can account for sample path asymmetries. It is shown that these models are capable of mimicking not only distributional skewness but also more complex geometrical asymmetries in the sample path such as tilting, front-back slope asymmetry and time irreversibility. Simple moment-based estimation techniques are briefly discussed to allow direct application to modelling and fitting actual records.

Suggested Citation

  • Anastassia Baxevani & Krzysztof Podgórski & Jörg Wegener, 2014. "Sample Path Asymmetries in Non-Gaussian Random Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1102-1123, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:1102-1123
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    File URL: http://hdl.handle.net/10.1111/sjos.12086
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    References listed on IDEAS

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    1. Zacharias Psaradakis, 2008. "Assessing Time‐Reversibility Under Minimal Assumptions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 881-905, September.
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