Constructing forecast models with regression, walk-forward, and robustness

Inputs and the target-variable

Forecast construction begins by choosing independent-variable series, transforming them into numeric inputs, and selecting a target-variable that is both usable in a later rule and realistically predictable from those inputs.

Preprocessing for shape, scale, and redundancy

A 26-session close window is converted into 25 successive-difference observations so first-layer inputs emphasize recent shape rather than absolute price level and so adjacent-level collinearity is reduced.

Inputs are expected to occupy a 0-to-1 range with a useful spread. A series that sits near one value except for rare extremes is treated as a poor preprocessing design.

A derived average should be omitted when the raw window that already determines it is present, because the extra series adds no information the mapping cannot extract from the originals.

Training and the fit statistic

Training repeatedly adjusts each interconnection-weight to improve agreement with the target-variable and stops when further passes add little. The fitted mapping is then scored on both the training facts and later unseen observations.

Squared-multiple-correlation, carried over from linear regression, is used as the preferred training and accuracy statistic because it uses all observations and estimates how much target-variable variation the forecast accounts for.

Convergence is judged by an r-squared path that rises and then plateaus. A sharp rise followed by a collapse is treated as a failed training process rather than a usable fit.

Walk-forward-holdout and the robustness-probe

After a stable in-sample plateau, the same accuracy statistics are recomputed on a later walk-forward-holdout to test whether the mapping generalizes. Failure on that later slice is treated as overfitting.

Robustness design keeps hidden capacity small, requires at least twice as many training facts as interconnections, and treats an in-sample r-squared above 0.90 as a warning of leakage or memorization.

A later holdout can fail even when training converged if the later market structure differs from the training window, so a robustness-probe includes asking whether the regime itself has changed.