Geodetic measurement data, characterized by multivariate time series, often deals with outliers and heavy stochastic variations. Previous research by the authors has proposed solutions combining nonlinear regression with autoregressive (AR) processes (Kargoll et al., J. Geodesy 92:271–297, 2018; Alkhatib et al., Further results on robust multivariate time series analysis in nonlinear models with autoregressive and t-distributed errors, Springer, pp. 25–38, 2018). We introduce an algorithm, based on Bayesian inference, robustly estimating functional parameters, AR coefficients, and t-distribution parameters, utilizing the Metropolis-within-Gibbs (MwG) approach for posterior density approximation. However, earlier validations of this MwG algorithm were mainly simulation-bound. Our research focuses on real-world scenarios and the analysis of this algorithm with respect to its robustness and accuracy. Through empirical studies, we seek to understand its potential and reliability, emphasizing a comprehensive vector-AR (VAR) process modeling.