In recent years, Graph Neural Networks (GNNs) have been leveraged for multivariate time series (MTS) analysis, as they effectively model inter-variable relationships, addressing a key limitation of deep learning methods. However, most existing GNN approaches for MTS classification construct a single static graph over the entire time series, neglecting that inter-variable dependencies vary over time. To address these limitations, we propose SkyGraph, a GNN-based framework that captures inter-variable dependencies across different temporal segments through phase partitioning and attention-based message passing. In addition, we employ masked mean pooling across time dimension to obtain robust phase-level representations, for MTS of varying lengths. These representations are then integrated through a transformer encoder to produce the final sample representation, suitable for both regression and classification tasks. The proposed framework is evaluated in the context of estimating hidden flight parameters, specifically the cost index (CI) and payload mass (PL). These parameters are essential inputs for Air Traffic Management (ATM), yet airlines keep them confidential as business-sensitive data. Our results show a clear reduction in mean absolute error compared to related approaches in regression tasks, and high accuracy in classification tasks. To assess the generalization capability of our architecture across domains, we further evaluate it on three diverse datasets from the UEA archive, achieving competitive performance against state-of-the-art methods. An ablation study conducted across both task types confirms that all architectural components contribute significantly to the model's performance.