Frequency Representations as Assumptions in Time-Series Learning

Abstract

This evidence synthesis examines representation-aware frequency analysis in time-series pipelines that use Fourier, Laplace, or wavelet transforms before prediction. It argues that the appropriate object of evaluation is the chain from temporal observation and transform through forecast distribution, calibration, local interpretation, and resource decision, not a model score in isolation. The review brings together the assigned studies with established work on uncertainty, robustness, provenance, and governance. Across these literatures, a common problem emerges: a representation or postprocessor can improve average error while distorting extremes, timing, or uncertainty that matter to decisions. The proposed framework separates evidence quality, model behavior, decision policy, and operational monitoring, then asks how each layer changes under distribution shift, adversarial pressure, or incomplete information. It recommends evaluation by slices and repeated trials, explicit reject and escalation policies, preservation of data and reasoning lineage, and prospective monitoring tied to defined actions. The result is a research agenda for systems that are efficient enough to use but also bounded enough to audit. No new experiment is claimed; the article develops a comparative conceptual model and identifies tests that would make future empirical claims more credible.