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We consider the problem of cross-validation (CV) in time series forecasting, with a focus on global forecasting models based on deep learning. The prevailing CV strategy in forecasting is to partition data across time with the last part of each series used for testing. With global models trained on collections of time series, however, a fundamentally different approach becomes possible: partitioning across series and time. We formalize series-wise CV for global forecasting models and benchmark several instantiations, including K-fold CV, bootstrapping, and Monte Carlo CV, on 11 datasets with 10 neural network architectures. We evaluate CV procedures along five dimensions: performance estimation, overoptimism rate, model selection accuracy, regret, and downstream forecasting performance. We withhold a random fraction of series from training so that they appear only in the test set. This protocol simulates the emergence of new series not seen during training, a common scenario in global forecasting. Under this protocol, our results reveal a nuanced trade-off: series-wise CV yields better downstream forecasting accuracy by guiding model selection toward configurations that generalize across both time and series, while time-wise CV retains a slight advantage for estimating out-of-sample error.