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AR(1) time series with autoregressive gamma variance for road topography modeling

Johannesson, Pär ; Podgorski, Krzysztof LU ; Rychlik, Igor and Shariati Fokalaei, Nima LU (2015) In Working Papers in Statistics
Abstract
A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) processwith randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal. A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed. The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressiveprocess is fitted from the autocorrelation of the squared values of the model. The shape parameter of the gamma distribution is fitted using the explicitly... (More)
A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) processwith randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal. A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed. The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressiveprocess is fitted from the autocorrelation of the squared values of the model. The shape parameter of the gamma distribution is fitted using the explicitly given moments of a generalized Laplace distribution.



Another general method of model fitting based on the correlation function of the signal is also presented and compared with the zero-crossing method. It is demonstrated that the model has the ability to accurately represent hilliness features of road topography providing a significant improvement over a purely (Less)
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author
; ; and
organization
publishing date
type
Working paper/Preprint
publication status
published
subject
keywords
Non-Gaussian time series, gamma distributed variances, generalized Laplace distribution, road surface profile, road roughness, road hilliness
in
Working Papers in Statistics
issue
5
pages
17 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
ccd18f9a-4224-4297-9de4-972238317ec3 (old id 8052703)
alternative location
http://journals.lub.lu.se/index.php/stat/article/view/15036
date added to LUP
2016-04-04 10:46:47
date last changed
2025-04-04 15:07:56
@misc{ccd18f9a-4224-4297-9de4-972238317ec3,
  abstract     = {{A non-Gaussian time series with a generalized Laplace marginal distribution is used to model road topography. The model encompasses variability exhibited by a Gaussian AR(1) processwith randomly varying variance that follows a particular autoregressive model that features the gamma distribution as its marginal. A simple estimation method to fit the correlation coefficient of each of two autoregressive components is proposed. The one for the Gaussian AR(1) component is obtained by fitting the frequency of zero crossing, while the autocorrelation coefficient for the gamma autoregressiveprocess is fitted from the autocorrelation of the squared values of the model. The shape parameter of the gamma distribution is fitted using the explicitly given moments of a generalized Laplace distribution.<br/><br>
<br/><br>
Another general method of model fitting based on the correlation function of the signal is also presented and compared with the zero-crossing method. It is demonstrated that the model has the ability to accurately represent hilliness features of road topography providing a significant improvement over a purely}},
  author       = {{Johannesson, Pär and Podgorski, Krzysztof and Rychlik, Igor and Shariati Fokalaei, Nima}},
  keywords     = {{Non-Gaussian time series; gamma distributed variances; generalized Laplace distribution; road surface profile; road roughness; road hilliness}},
  language     = {{eng}},
  note         = {{Working Paper}},
  number       = {{5}},
  publisher    = {{Department of Statistics, Lund university}},
  series       = {{Working Papers in Statistics}},
  title        = {{AR(1) time series with autoregressive gamma variance for road topography modeling}},
  url          = {{https://lup.lub.lu.se/search/files/5619212/8054215.pdf}},
  year         = {{2015}},
}