The generation of synthetic turbulence time series using data-driven models has gained considerable attention as an alternative to standard numerical simulation for analysis, forecasting, and reduced-order modeling. While validation of such models typically focuses on low-order statistics, these metrics alone provide limited insight into whether the temporal dependencies and physical interactions inherent to turbulence are faithfully preserved. In particular, the preservation of both linear and nonlinear couplings across spatial locations remains insufficiently explored. In this study, we evaluate the ability of a high-order linear vector autoregressive (VAR) model to reproduce interaction dynamics in turbulent channel flow velocity time series sampled at multiple wall-normal locations. Linear dependencies are quantified using auto- and cross-covariance functions, while nonlinear interactions are assessed through information-theoretic measures [2], including time-delayed mutual information and transfer entropy. These diagnostics are applied consistently to both the simulation turbulence data and the corresponding synthetic time series generated by the VAR model. The results [1] demonstrate that the VAR framework accurately preserves linear interaction structures, even for time series exhibiting long memory. In contrast, nonlinear interaction measures reveal a systematic degradation in quantitative accuracy, with transfer entropy magnitudes being underestimated. Nevertheless, the dominant direction of information transfer between paired signals is correctly identified in most cases. Moreover, when state-space embeddings are constructed using optimal parameters, the inferred net information transfer aligns with established physical causality in wall bounded turbulence. These findings highlight the importance of complementing traditional statistical validation with interactionbased diagnostics when assessing synthetic turbulence time series. The proposed evaluation framework provides a physically interpretable means of determining whether data-driven models reproduce not only marginal statistics, but also the underlying dynamical relationships. The approach is readily extendable to multivariate turbulence data generated by alternative modeling strategies, including nonlinear and machine-learning-based methods.