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Deep learning approaches achieve outstanding predictive performance inmodeling modern data, despite the increasing complexity and scale. However,evaluating the quality of predictive models becomes more challenging, astraditional statistical assumptions often no longer hold. In particular,spatio-temporal data exhibit dependencies across both time and space, ofteninvolving nonlinear dynamics, non-stationarities, and missing observations. Asa result, advanced predictors such as spatio-temporal graph neural networksrequire novel evaluation methodologies. This paper introduces a residualcorrelation analysis framework designed to assess the optimality ofspatio-temporal predictive neural models, particularly in scenarios withincomplete and heterogeneous data. By leveraging the principle that residualcorrelation indicates information not captured by the model, this frameworkserves as a powerful tool to identify and localize regions in space and timewhere model performance can be improved. A key advantage of the proposedapproach is its ability to operate under minimal assumptions, enabling robustevaluation of deep learning models applied to multivariate time series, even inthe presence of missing and heterogeneous data. The methodology employstailored spatio-temporal graphs to encode sparse spatial and temporaldependencies within the data and utilizes asymptotically distribution-freesummary statistics to pinpoint time intervals and spatial regions where themodel underperforms. The effectiveness of the proposed residual analysis isdemonstrated through validation on both synthetic and real-world scenariosinvolving state-of-the-art predictive models.

Assessment of Spatio-Temporal Predictors in the Presence of Missing and Heterogeneous Data