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**Harvard**

Johannesson, P., Krzysztof, P., Rychlik, I. och Shariati, N. (2016) *AR(1) time series with autoregressive gamma variance for road topography modeling*.

** BibTeX **

@article{

Johannesson2016,

author={Johannesson, Pär and Krzysztof, Podgorski and Rychlik, Igor and Shariati, Nima},

title={AR(1) time series with autoregressive gamma variance for road topography modeling},

journal={Probabilistic Engineering Mechanics},

issn={0266-8920},

volume={43},

pages={106-116},

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) process with 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 autoregressive process 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 Gaussian model.},

year={2016},

keywords={Non-Gaussian time series, Gamma distributed variances, Generalized Laplace distribution, Road surface profile, Road roughness, Road hilliness},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 231018

A1 Johannesson, Pär

A1 Krzysztof, Podgorski

A1 Rychlik, Igor

A1 Shariati, Nima

T1 AR(1) time series with autoregressive gamma variance for road topography modeling

YR 2016

JF Probabilistic Engineering Mechanics

SN 0266-8920

VO 43

SP 106

OP 116

AB 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) process with 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 autoregressive process 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 Gaussian model.

LA eng

DO 10.1016/j.probengmech.2015.12.006

LK http://dx.doi.org/10.1016/j.probengmech.2015.12.006

OL 30