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

Johannesson, Pär; Podgórski, Krzysztof; Rychlik, Igor; Fokalaei, Nima Shariati

doi:10.1016/j.probengmech.2015.12.006

Cited by 20 publications

(17 citation statements)

References 14 publications

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“…Furthermore, one can assume Gaussian distribution model with random variance such as generalized Laplace or generalized hyperbolic distributions. An example of such non Gaussian time series model is presented by Johannesson et al (2016)…”

Section: Appendix Amentioning

confidence: 99%

Robust residual control chart for contaminated time series: A solution to the effects of outlier-driven parameter misestimation on the control chart performance

Shariati

2020

Communications in Statistics - Theory and Methods

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Control charts have typically been constructed using estimators obtained under assumptions of data independence and a given distribution of data. Here, I deal with cases in which neither of these conditions are satisfied. In particular, I consider the case of data obtained from a first-order autoregressive (AR(1)) time series model that have been contaminated by outlying process observations. I first analyze the effects of contaminations on the accuracy of estimation of parameters and control limits, and thus on the performance of time-series control charts. Next, I present a novel design for a robust control chart suitable for autocorrelated observations that is robust against the effects of contaminations. The proposed chart is based on an innovative approach to parameter estimation of autocorrelated data based on our previously developed Iteratively Robust Filtered Fast-s estimation method. This chart is shown to outperform the classical control charts' ability to detect structural changes, including changes in the process mean and in the variance of errors. This improvement in performance, as measured by Average Run Length and Mean Squared Deviation, is verified in a simulation study. This method has clear potential to improve control charts for applications whereby the data being monitored is both autocorrelated and contaminated. ARTICLE HISTORY

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Section: Appendix Amentioning

confidence: 99%

Robust residual control chart for contaminated time series: A solution to the effects of outlier-driven parameter misestimation on the control chart performance

Shariati

2020

Communications in Statistics - Theory and Methods

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“…Once the model is fitted to the data it can be utilized in dedicated programs to simulate fuel consumption of vehicles as well as to estimate energy losses. In fact, the presented study was initiated by investigations of efficiency of different technical solutions to harvest energy from breaking and driving downhills of utility vehicles in mines, see (Johannesson et al, 2015b). The empirical example that is used in this paper to illustrate the proposed model is based on topography records from a road surface segment in a mine.…”

Section: Topographymentioning

confidence: 99%

“…The degree of dependence is a function of the chosen length of the constant variance segments (here 25 metres). In (Johannesson et al, 2015b) an autoregressive model for the normalized variances R k was suggested. The model has one regression parameter a r , and it can been shown that it has exponentially decaying autocorrelation a k r , k = 0, 1, .…”

Section: Laplace Model With Correlated Variancesmentioning

confidence: 99%

Laplace distribution models for road topography and roughness

Johannesson¹,

Podgórski

Rychlik

2017

IJVP

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“…In 1990 Sim, C. H. [22] studied Gamma and Exponential autoregressive process. Johannesson et al [13] also studied autoregressive model with gamma variance for road topography modelling. Berger, K. et al [1] has done studied on goodness of fit measures for model evaluation.…”

Section: Introductionmentioning

confidence: 99%

Gaussian and Non-Gaussian Autoregressive Time Series Models with Rainfall Data

Kaur¹,

Rakshit²

2019

IJEAT

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The Gaussian and non- Gaussian autoregressive models are used in this paper for analyzing time series data. The autoregressive time series models with various distributions are considered here for analyzing the annual rainfall of Punjab, India. Three different types of autoregressive models are applied here for analyzing data namely autoregressive model with Gaussian, Gamma and Laplace distribution. For the goodness of fit the chi - square test is applied and the best fitted distribution is obtained for the data. Next the stationarity of data is checked, after that models are applied on data for comparing three distributions of AR models and lastly the best fitted model is obtained. The residual checking of selected model is also discussed and forecast the best fitted model based on simulated response comparison.

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

Cited by 20 publications

References 14 publications

Robust residual control chart for contaminated time series: A solution to the effects of outlier-driven parameter misestimation on the control chart performance

Robust residual control chart for contaminated time series: A solution to the effects of outlier-driven parameter misestimation on the control chart performance

Laplace distribution models for road topography and roughness

Gaussian and Non-Gaussian Autoregressive Time Series Models with Rainfall Data

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