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VOLATILITY FORECASTING FROM ECONOMETRICS TO ARTIFICIAL INTELLIGENCE: A FOUR-STAGE REVIEW OF THE EVIDENCE PIPELINE FROM FORECAST ACCURACY TO PORTFOLIO PERFORMANCE
A volatility forecast becomes useful only after it has passed through four stages: a model produces it, a trading rule consumes it, a portfolio aggregates the result, and an investor evaluates that result against a utility function. Each stage has its own mature evaluation apparatus, and each is studied in isolation. This review traces the forecast through the whole pipeline and asks where the evidence connecting the stages actually exists. Drawing on 153 studies published between 1963 and 2026, covering both the international and the Russian-language literature, it makes four contributions. First, it introduces the four-stage pipeline itself as an organising framework for a literature that has never been surveyed across, rather than within, its stages. Second, it develops a classification of the channels through which a forecast reaches a trading decision — trade parameters, entry gating, position sizing and allocation. The first three channels and their comparative evaluation were introduced by the author in Lysenok (2026a); the framework is generalised here to four channels and applied as an organising instrument for the literature, which is shown to be structured one channel at a time, with no comparison under common conditions. Third, it maps the state of the evidence stage by stage and reports a quantitative asymmetry: 81 of the 153 studies evaluate forecasts by a statistical loss alone, 35 evaluate trading or portfolio outcomes without reference to forecast quality, and only 8 apply both criteria. The only direct comparison of channels under common conditions is the author's own, and its results — gains concentrated entirely in the channels that govern the commitment of capital, with the trade-parameter channel delivering no measurable economic value — indicate that the transitions this review maps are not formalities. Fourth, it systematises for an international readership a body of Russian-language work on volatility forecasting that has remained inaccessible behind a language barrier. The review concludes that statistical accuracy is a defensible proxy for economic value only conditionally on the channel through which the forecast reaches the allocation of capital, and sets out five research tasks that follow from the mapping.