The current study focuses on a multilevel extension of the autoregressive (AR) model, the Multilevel First-Order Autoregressive Model (ML-AR(1)).  The ML-AR(1) model allows for the study of between-object differences in the parameters of the AR-model. These differences can provide valuable information. For example, they allow for the estimation and further investigation of differences in stability and sensitivity of the amount of trade of companies and/or cities. Two Bayesian Estimation methods for the ML-AR(1) model are introduced, which are compared to three standard Maximum Likelihood estimation methods in an extensive simulation study. Benefits of the Bayesian methods compared to the Maximum Likelihood methods are discussed, like the ability to model individual differences in sensitivity to external influences.