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Decision-making with deep learning-based time series forecasting requires not only accurate predictions but also actionable insights. However, current architectures do not inherently provide such information. Specifically, guidance is needed on how current conditions must be modified to shift from a predicted outcome to a desired future scenario. Counterfactual explanations provide a natural framework for this task, as they represent minimal input changes that alter the model's prediction, indicating when and how intervention is required. Existing approaches rely on instance-wise optimization, leading to inconsistency across instances, high computational costs, and limited applicability in real-time settings. To address these limitations, we reformulate counterfactual generation for time series forecasting as the problem of learning a globally consistent intervention strategy, allowing counterfactuals to be generated through a single shared function. We propose Counterfactual Time Series Explanations (ConTex), a model-agnostic, decomposed architecture comprising a temporal context encoder and a conditional encoder, followed by two heads that capture interventions in terms of temporal relevance and modification strength. This structure overcomes the instability and inconsistency of instance-based approaches by producing targeted, interpretable interventions across time and feature dimensions in a single forward pass, making it suitable for real-time applications. Across multiple forecasting architectures and benchmark datasets, ConTex achieves state-of-the-art validity while generating sparse counterfactuals that minimize the number of necessary interventions. Additionally, our approach reduces computational cost by at least 12-36x compared to instance-wise generation and supports real-time inference at approximately 0.007 seconds.