Advanced

Slepian noise approach for gaussian and Laplace moving average processes

Podgorski, Krzysztof LU ; Rychlik, Igor and Wallin, Jonas (2015) In Extremes 18(4). p.665-695
Abstract
Slepian models are derived for a stochastic process observed at level crossings of a moving average driven by a gaussian or Laplace noise. In particular, a Slepian model for the noise – the Slepian noise – is developed. For Laplace moving average process a method of sampling from the Slepian noise is also obtained by a Gibbs sampler. This facilitates comparison of behavior at crossing of a level between a gaussian process and a non-gaussian one and allows to study a random processes sampled at crossings of a non-gaussian moving average process. In a numerical study based on the method it is observed that the behavior of a non-gaussian moving average process at high level crossings is fundamentally different from that for the gaussian case,... (More)
Slepian models are derived for a stochastic process observed at level crossings of a moving average driven by a gaussian or Laplace noise. In particular, a Slepian model for the noise – the Slepian noise – is developed. For Laplace moving average process a method of sampling from the Slepian noise is also obtained by a Gibbs sampler. This facilitates comparison of behavior at crossing of a level between a gaussian process and a non-gaussian one and allows to study a random processes sampled at crossings of a non-gaussian moving average process. In a numerical study based on the method it is observed that the behavior of a non-gaussian moving average process at high level crossings is fundamentally different from that for the gaussian case, which is in line with some recent theoretical results on the subject. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Rice formula Level crossings, Generalized Laplace distribution, Moving average process, Extreme episodes, Tilted Rayleigh distribution, Generalized inverse gaussian distribution
in
Extremes
volume
18
issue
4
pages
665 - 695
publisher
Kluwer
external identifiers
  • wos:000364634500006
  • scopus:84946496265
ISSN
1572-915X
DOI
10.1007/s10687-015-0227-z
language
English
LU publication?
yes
id
e8b540b2-94a3-47b7-a9c4-1c5e45619650 (old id 8228312)
date added to LUP
2015-11-20 15:13:07
date last changed
2017-01-01 03:27:04
@article{e8b540b2-94a3-47b7-a9c4-1c5e45619650,
  abstract     = {Slepian models are derived for a stochastic process observed at level crossings of a moving average driven by a gaussian or Laplace noise. In particular, a Slepian model for the noise – the Slepian noise – is developed. For Laplace moving average process a method of sampling from the Slepian noise is also obtained by a Gibbs sampler. This facilitates comparison of behavior at crossing of a level between a gaussian process and a non-gaussian one and allows to study a random processes sampled at crossings of a non-gaussian moving average process. In a numerical study based on the method it is observed that the behavior of a non-gaussian moving average process at high level crossings is fundamentally different from that for the gaussian case, which is in line with some recent theoretical results on the subject.},
  author       = {Podgorski, Krzysztof and Rychlik, Igor and Wallin, Jonas},
  issn         = {1572-915X},
  keyword      = {Rice formula Level crossings,Generalized Laplace distribution,Moving average process,Extreme episodes,Tilted Rayleigh distribution,Generalized inverse gaussian distribution},
  language     = {eng},
  number       = {4},
  pages        = {665--695},
  publisher    = {Kluwer},
  series       = {Extremes},
  title        = {Slepian noise approach for gaussian and Laplace moving average processes},
  url          = {http://dx.doi.org/10.1007/s10687-015-0227-z},
  volume       = {18},
  year         = {2015},
}