Sample Path Asymmetries in Non-Gaussian Random Processes

Anastassia Baxevani, Krzysztof Podgorski, Jörg Wegener

Research output: Contribution to journalArticlepeer-review

6 Citations (SciVal)

Abstract

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.
Original languageEnglish
Pages (from-to)1102-1123
JournalScandinavian Journal of Statistics
Volume41
Issue number4
DOIs
Publication statusPublished - 2014

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • Laplace distribution
  • Matern covariance
  • moving average processes
  • Rice
  • formula
  • stationary second-order processes
  • tilting
  • time
  • irreversibility

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