On Unlearning for Time-series Forecasting

Time-series forecasting is widely used in healthy, transportation, finance, and many other domains. Models in these settings are often trained on longitudinal user or entity level records, which may later require removal because they contain sensitive or proprietary information or have been corrupted by sensor failures. To address such deletion requests without costly retraining, machine unlearning has been widely studied as a practical mechanism for privacy protection and data governance. However, the application of machine unlearning to time series prediction has not yet been well realized, it mainly dues to the following unique challenges: Gradient-based unlearning can be unstable because a deleted observation participates in multiple causally connected forecasting windows, causing parameter updates to propagate beyond the requested interval and degrade retained forecasting utility. Label-guided updating offers a more controlled alternative, but continuous and context-dependent forecasts lack a suitable replacement target, while the exact-retrained output is unavailable during unlearning. Moreover, the remaining support for a deleted temporal pattern is highly non-uniform. Some affected windows retain structurally similar counterparts in the retained data, whereas others become underrepresented or isolated. We present RDTU, a Residual Diffusion framework of Time-series Unlearning that constructs labels without accessing an exact-retrained model at unlearning time. RDTU first uses a retained-set neural tangent kernel predictor to obtain a deletion-compatible base forecast. Then it quantifies the global and local structural support of each affected window using the volume contribution of the retained-reference data. Conditioned on the query window, retained-set prediction, and structural support, a diffusion model generates a residual correction that estimates the counterfactual forecast, yielding a pseudo-label field that guides a lightweight model update. Experiments across real-world forecasting benchmarks show that RDTU consistently produces unlearned models that most closely match exact retraining among the evaluated efficient unlearning methods. It achieves this alignment while maintaining retained forecasting utility and reducing membership-inference signals.