Identifying the correct stochastic model in GNSS time series is essential to study geophysical parameters such as site velocities, and hence enhancing their accuracy. The rate uncertainty is a critical aspect in GNSS time series analysis. The variance component estimation (VCE) methods commonly utilize unconstrained estimation principles. Simulating 1000-time series for 4 different noise combinations with 10 years’ time span, we have investigated the performance of non-negative least squares VCE (NNLS-VCE) method for identifying an appropriate noise model. Our results are provided for both univariate and multivariate analysis. As the noise model's complexity increases, the significance of employing multivariate analysis is prominent in contrast to univariate analysis. After thorough analysis, we have determined that treating the false-positive model as a stochastic model in time series yields significant insights. Specifically, if the accumulative spectral index is lower than the true value, it results in an underestimation of the rate uncertainty. Conversely, if the index is higher than the actual value, it leads to an overestimation. Additionally, we observed that as the noise model complexity increases, the number of false-positive models also increases. However, the implementation of multivariate analysis mitigates this increase, offering a more realistic and reliable approach. In case of four distinct noise models, the detection power percentages of 98.5%, 90.5%, 69.5%, 29.3% of univariate analysis increased to 99.5%, 99.8%, 88.4% and 83.7% for multivariate analysis.