Premium
Sample Path Asymmetries in Non‐Gaussian Random Processes
Author(s) -
Baxevani Anastassia,
Podgórski Krzysztof,
Wegener Jörg
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12086
Subject(s) - skewness , mathematics , asymmetry , statistical physics , sample (material) , gaussian , path (computing) , econometrics , moment (physics) , statistics , computer science , chemistry , physics , chromatography , quantum mechanics , classical mechanics , programming language
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.