Temporal Structural Forecasting: Constructing the {4,5,6} Forecast Distribution Object

Forecasting exists to address the timing problem: when to act. Every published time series method identifies what the next value will be instead, because every one of them performs a Unidimensional Univariate (UU) Operation: the method discards the calendar date attached to each historical observation and returns a value indexed by no calendar date, for which no probability distribution is selected (Burk 2026d). The Theory of Temporal Forecasting establishes the object a forecast must return in its place, the {4,5,6} Forecast Distribution Object: a Dimension 4 forecast value, the Dimension 5 Probability distribution at the seasonal position of a calendar date, and that Dimension 6 calendar date. No single UU Operation returns one. Temporal Structural Forecasting is the methodology that constructs it. Two UU Operations run along two orthogonal timelines, one sequential and one seasonal, and Orthogonal Recovery combines their outputs into a forecast value at a calendar date. The record of relative errors at each seasonal position recovers the distribution at that position as the Calibrated Probability Band, which at each calibration is the normal range at that date. Selection among competing Temporal Forecasting Models by the width of their bands at each date produces, across a forecast horizon, the Map of Normal: a specification of what counts as normal at every calendar date, committed before any realized value arrives. Because every input to a {4,5,6} Forecast Distribution Object predates the calendar date it describes, no pathway exists for an outcome to enter the computation that specified it.