Do Time Series Foundation Models Use Imputed Values?

Forecasting pipelines impute missing histories for time series foundation models. Do better reconstructions improve forecasts? The answer depends on both computational access and learned use. We probe eighteen checkpoints from eleven families through their missingness interfaces, paths combining fills with observation indicators. Ten of the eighteen checkpoints block position-specific fill content on their declared paths. In Chronos-Bolt, masking retains dependence on the context mean and standard deviation but removes this content, explaining why even exact fills recover little forecast accuracy under scattered and block missingness. More generally, an interface bound characterises an imputer’s access to the forecast, which is distinct from learned use in paired pretraining experiments. Gap exposure can improve accuracy without responding to fill quality, whereas repair-aware training makes retained content useful. Our retrofit passes fills with observation flags and learns across gap mechanisms and repair qualities. After 5,000 continued-pretraining steps, it reduces zero- and linear-fill degradation relative to complete-context error across three families, with little change on complete histories. On nine GIFT-Eval subsets with recorded gaps, the retrofit lowers median MASE by up to 18% in high-missingness windows. Our code is available at https://anonymous.4open.science/r/hole-in-input-repro-2E97/README.md.