Details
| Original language | English |
|---|---|
| Article number | 20 |
| Journal | Engineering Proceedings |
| Volume | 5 |
| Issue number | 1 |
| Publication status | Published - 28 Jun 2021 |
Abstract
Keywords
- AR process, GNSS time series, multivariate time series, nonlinear Bayesian regression model, partially adaptive estimation, robust parameter estimation, scaled t-distribution
ASJC Scopus subject areas
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Electrical and Electronic Engineering
- Engineering(all)
- Industrial and Manufacturing Engineering
- Engineering(all)
- Biomedical Engineering
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Engineering Proceedings, Vol. 5, No. 1, 20, 28.06.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bayesian Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors
AU - Dorndorf, Alexander
AU - Kargoll, Boris
AU - Paffenholz, Jens-André
AU - Alkhatib, Hamza
N1 - Publisher Copyright: © 2021 by the authors.
PY - 2021/6/28
Y1 - 2021/6/28
N2 - Many geodetic measurement data can be modelled as a multivariate time series consisting of a deterministic (“functional”) model describing the trend, and a stochastic model of the correlated noise. These data are also often affected by outliers and their stochastic properties can vary significantly. The functional model of the time series is usually nonlinear regarding the trend parameters. To deal with these characteristics, a time series model, which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance-stationary autoregressive (AR) processes the white noise components of which obey independent, scaled t-distributions, was proposed by the authors in previous research papers. In this paper, we extend the aforementioned model to include prior knowledge regarding various model parameters, the information about which is often available in practical situations. We develop an algorithm based on Bayesian inference that provides a robust and reliable estimation of the functional parameters, the coefficients of the AR process and the parameters of the underlying t-distribution. We approximate the resulting posterior density using Markov chain Monte Carlo (MCMC) techniques consisting of a Metropolis-within-Gibbs algorithm.
AB - Many geodetic measurement data can be modelled as a multivariate time series consisting of a deterministic (“functional”) model describing the trend, and a stochastic model of the correlated noise. These data are also often affected by outliers and their stochastic properties can vary significantly. The functional model of the time series is usually nonlinear regarding the trend parameters. To deal with these characteristics, a time series model, which can generally be explained as the additive combination of a multivariate, nonlinear regression model with multiple univariate, covariance-stationary autoregressive (AR) processes the white noise components of which obey independent, scaled t-distributions, was proposed by the authors in previous research papers. In this paper, we extend the aforementioned model to include prior knowledge regarding various model parameters, the information about which is often available in practical situations. We develop an algorithm based on Bayesian inference that provides a robust and reliable estimation of the functional parameters, the coefficients of the AR process and the parameters of the underlying t-distribution. We approximate the resulting posterior density using Markov chain Monte Carlo (MCMC) techniques consisting of a Metropolis-within-Gibbs algorithm.
KW - AR process
KW - GNSS time series
KW - multivariate time series
KW - nonlinear Bayesian regression model
KW - partially adaptive estimation
KW - robust parameter estimation
KW - scaled t-distribution
UR - http://www.scopus.com/inward/record.url?scp=85145404842&partnerID=8YFLogxK
U2 - 10.3390/engproc2021005020
DO - 10.3390/engproc2021005020
M3 - Article
VL - 5
JO - Engineering Proceedings
JF - Engineering Proceedings
IS - 1
M1 - 20
ER -