TY - JOUR

T1 - Self-tuning robust adjustment within multivariate regression time series models with vector-autoregressive random errors

AU - Kargoll, Boris

AU - Kermarrec, Gaël

AU - Korte, Johannes

AU - Alkhatib, Hamza

N1 - Funding Information: Open Access funding provided by Projekt DEAL. This research was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project No. 386369985. The authors gratefully acknowledge the EUREF Permanent Network (EPN) and corresponding agencies for freely providing the data.

PY - 2020/5/10

Y1 - 2020/5/10

N2 - The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables measured contemporaneously. The proposed approaches allow for the modeling of both auto- and cross-correlations through a vector-autoregressive (VAR) process, where the components of the white-noise input vector are modeled at every time instance either as stochastically independent t-distributed (herein called “stochastic model A”) or as multivariate t-distributed random variables (herein called “stochastic model B”). Both stochastic models are complementary in the sense that the former allows for group-specific degrees of freedom (df) of the t-distributions (thus, sensor-component-specific tail or outlier characteristics) but not for correlations within each white-noise vector, whereas the latter allows for such correlations but not for different dfs. Within the observation equations, nonlinear (differentiable) regression models are generally allowed for. Two different generalized expectation maximization (GEM) algorithms are derived to estimate the regression model parameters jointly with the VAR coefficients, the variance components (in case of stochastic model A) or the cofactor matrix (for stochastic model B), and the df(s). To enable the validation of the fitted VAR model and the selection of the best model order, the multivariate portmanteau test and Akaike’s information criterion are applied. The performance of the algorithms and of the white noise test is evaluated by means of Monte Carlo simulations. Furthermore, the suitability of one of the proposed models and the corresponding GEM algorithm is investigated within a case study involving the multivariate modeling and adjustment of time-series data at four GPS stations in the EUREF Permanent Network (EPN).

AB - The iteratively reweighted least-squares approach to self-tuning robust adjustment of parameters in linear regression models with autoregressive (AR) and t-distributed random errors, previously established in Kargoll et al. (in J Geod 92(3):271–297, 2018. https://doi.org/10.1007/s00190-017-1062-6), is extended to multivariate approaches. Multivariate models are used to describe the behavior of multiple observables measured contemporaneously. The proposed approaches allow for the modeling of both auto- and cross-correlations through a vector-autoregressive (VAR) process, where the components of the white-noise input vector are modeled at every time instance either as stochastically independent t-distributed (herein called “stochastic model A”) or as multivariate t-distributed random variables (herein called “stochastic model B”). Both stochastic models are complementary in the sense that the former allows for group-specific degrees of freedom (df) of the t-distributions (thus, sensor-component-specific tail or outlier characteristics) but not for correlations within each white-noise vector, whereas the latter allows for such correlations but not for different dfs. Within the observation equations, nonlinear (differentiable) regression models are generally allowed for. Two different generalized expectation maximization (GEM) algorithms are derived to estimate the regression model parameters jointly with the VAR coefficients, the variance components (in case of stochastic model A) or the cofactor matrix (for stochastic model B), and the df(s). To enable the validation of the fitted VAR model and the selection of the best model order, the multivariate portmanteau test and Akaike’s information criterion are applied. The performance of the algorithms and of the white noise test is evaluated by means of Monte Carlo simulations. Furthermore, the suitability of one of the proposed models and the corresponding GEM algorithm is investigated within a case study involving the multivariate modeling and adjustment of time-series data at four GPS stations in the EUREF Permanent Network (EPN).

KW - Cross-correlations

KW - Generalized expectation maximization algorithm

KW - GPS time series

KW - Iteratively reweighted least squares

KW - Monte Carlo simulation

KW - Multivariate portmanteau test

KW - Multivariate scaled t-distribution

KW - Regression time series

KW - Self-tuning robust estimator

KW - Vector-autoregressive model

UR - http://www.scopus.com/inward/record.url?scp=85084301517&partnerID=8YFLogxK

U2 - 10.1007/s00190-020-01376-6

DO - 10.1007/s00190-020-01376-6

M3 - Article

AN - SCOPUS:85084301517

VL - 94

JO - Journal of Geodesy

JF - Journal of Geodesy

SN - 0949-7714

IS - 5

M1 - 51

ER -