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Sample Path Asymmetries in Non-Gaussian Random Processes

Baxevani, Anastassia; Podgorski, Krzysztof LU and Wegener, Jörg LU (2014) In Scandinavian Journal of Statistics 41(4). p.1102-1123
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,... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Laplace distribution, Matern covariance, moving average processes, Rice, formula, stationary second-order processes, tilting, time, irreversibility
in
Scandinavian Journal of Statistics
volume
41
issue
4
pages
1102 - 1123
publisher
Wiley-Blackwell
external identifiers
  • wos:000344860800014
  • scopus:84920363206
ISSN
1467-9469
DOI
10.1111/sjos.12086
language
English
LU publication?
yes
id
cab6c6b4-6073-4b6f-a405-a74b924e7221 (old id 4982973)
date added to LUP
2015-01-27 10:40:36
date last changed
2017-01-01 04:01:23
@article{cab6c6b4-6073-4b6f-a405-a74b924e7221,
  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.},
  author       = {Baxevani, Anastassia and Podgorski, Krzysztof and Wegener, Jörg},
  issn         = {1467-9469},
  keyword      = {Laplace distribution,Matern covariance,moving average processes,Rice,formula,stationary second-order processes,tilting,time,irreversibility},
  language     = {eng},
  number       = {4},
  pages        = {1102--1123},
  publisher    = {Wiley-Blackwell},
  series       = {Scandinavian Journal of Statistics},
  title        = {Sample Path Asymmetries in Non-Gaussian Random Processes},
  url          = {http://dx.doi.org/10.1111/sjos.12086},
  volume       = {41},
  year         = {2014},
}