Improving Conditional Coverage in Time-Series Foundation Models via Direct Volatility Modeling

Time-series foundation models (TSFMs) provide probabilistic forecasts and are often reported to be well calibrated when evaluated via marginal coverage. However, forecast errors in time series are typically serially dependent and heteroskedastic, so marginal calibration can mask substantial regime-dependent miscalibration. We show empirically that prediction intervals from several TSFMs systematically under-cover during high-volatility periods, despite achieving near-nominal coverage on average. To account for this heteroskedasticity, we consider two post hoc adjustments: adaptive conformal prediction and a model-based approach that directly models time-varying residual variance using GARCH. Our analysis shows that direct volatility modeling yields markedly improved conditional calibration of TSFMs across four real-world datasets. These findings highlight the need to treat predictive variance as an evolving process when training TSFMs.