A Conceptual framework for reliable Time – Series Forecasting: Adaptive Preprocessing with Conformal Uncertainty Guarantees

Time-series forecasting models typically rely on an implicit assumption about the prior distribution of the data. When this assumption does not match reality—i.e., when an "incompatible prior" is in effect—the model's performance severely degrades, and its confidence interval coverage (e.g., 95%) systematically decreases. This paper presents a novel conceptual framework that directly addresses this issue. The core of the framework is a two-stage adaptive process: first, an online adaptive preprocessing module neutralizes the effect of an unknown or disruptive prior by identifying and removing dominant non-stationary structures (such as trend and seasonality), transforming the data into a stationary space. Then, in this stationary space, a simple probabilistic model is used for forecasting. To ensure reliability, a post-processing calibration layer based on Conformal Prediction is added to produce confidence intervals with statistically guaranteed confidence levels (e.g., 95%). This paper focuses on the theoretical foundation, mathematical guarantees, and qualitative behavior of this framework. Experimental results on synthetic data with increasing levels of complexity confirm the achievement of target coverage and the system's intelligent behavior (such as automatically increasing uncertainty at discontinuities and handling outliers).