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Effective resource allocation in telecommunication networks can benefit from accurate demand forecasting to optimize performance and prevent inefficiencies such as resource over-provisioning or shortages. Traditional forecasting approaches often fail to capture uncertainty and multivariate interdependencies. This frequently results in suboptimal decision-making, particularly in dynamic, multi-tenant environments such as Open Radio Access Networks (O-RAN). To mitigate this issue, multivariate probabilistic forecasting provides a more robust approach by capturing the interdependencies among multiple resource time series, including but not limited to PRB, and by providing confidence intervals for predictions, enabling more adaptive and reliable resource management in O-RAN. This paper proposes a cloud-native resource allocation framework for O-RAN, integrating advanced probabilistic forecasting models within RAN Intelligent Controllers (RICs). We implement and evaluate Gaussian Process Vector Autoregression (GPVAR) and Temporal Fusion Transformer (TFT), comparing their performances against multivariate Long Short-Term Memory (LSTM) networks. The proposed solutions are deployed as a containerized radio application (rApp) and integrated with Swagger's REST API to facilitate network exposure & seamless deployment within the O-RAN framework. Through extensive experiments, we demonstrate that for longer time series, TFT provides accurate and reliable forecasts, particularly in dynamic multi-tenant scenarios. In contrast, GPVAR offers better performance and a strong balance between accuracy and computational efficiency for shorter time series. Additionally, we investigate low-rank approximations in GPVAR, showing that mid-range rank configurations optimize computational complexity while maintaining predictive performance. We also analyze the computational trade-offs, showing that TFT incurs higher training costs but offers faster inference and lower resource overhead compared to GPVAR and LSTM. By bridging theoretical research with practical O-RAN deployment, this work provides a robust foundation for AI-driven resource management in next-generation networks. © 2013 IEEE.