Constructing walk-forward forecasts with linear and moving-average baselines

Lock the construction before search

Linear statistical single-market constructions that historically simulated and backtested a market against its own past prices were described as the prevailing technical baseline of the prior decade. The modeling task was classified as prediction of price or trend, so candidate architectures were judged by whether they emitted a future value from ordered observations.

Editorial reading: write the linear-regression baseline and the moving-average lookback recipe first. After those pieces are locked, change only hidden-layer capacity inside a walk-forward holdout.

Write the linear-regression baseline

Linear-regression is an explicit linear mapping from ordered price, volume, or breadth observations to a forecast, kept as the quantitative baseline that later nonlinear constructions must beat out of sample. Those linear statistical single-market constructions were described as the prevailing technical baseline of the prior decade.

A forecast construction was allowed to combine technical, intermarket, and fundamental series in one mapping rather than restricting inputs to a single market's own past prices.

Place moving averages in the input-vector

A moving-average is a fixed-lookback summary of an ordered price, volume, or open-interest series that occupies one coordinate of the input-vector. Moving averages of prices, volume, and open interest were listed among the ordered series presented at the input layer of a multilayer forecast mapping.

The input-vector is the fixed-length bundle of contemporaneous features presented as one training or test fact. A feedforward construction had to encode lookback inside each input-vector, whereas a recurrent construction could receive one observation per step and learn temporal dependence from presentation order.

Two worked forecast mappings

One worked construction mapped a three-part input, high-low differences over the prior two days plus a five-day moving average of closes, onto the next day's median price.

For a close-change forecast built from five-day moving averages of the close, high, and low, the layout used three input units, one output unit, and at least one hidden-layer.

Search only hidden-layer capacity

A hidden-layer is an intermediate processing stage whose unit count is a construction choice found by search, not a market observation. Hidden-unit count was treated as a search variable, with a suggested start between half and twice the number of inputs, because too many hidden units fit the training facts and failed on unseen test facts.

That failure is overfitting: extra hidden capacity that reproduces training facts and then fails on facts withheld for testing. After each forward pass, output error was sent backward through the layers to adjust connection weights, and facts were reused until residual error reached a level the designer judged acceptable. Zero error was treated as unrealistic for market data.

Editorial vocabulary: a transfer-function is a smooth nonlinear map applied after a weighted sum so the constructed model can represent curved input-output relationships.

Data selection, preprocessing, training-parameter search, and the testing procedure were all said to control whether a constructed model generalized, so no single architectural setting was treated as sufficient.

Score later unseen facts

Walk-forward-analysis is a single testable procedure that trains on an earlier window and scores only later unseen facts, so entry, exit, and abstention rules are judged together.

Editorial reading: after the linear-regression baseline and the moving-average lookback recipe are written, change only hidden-layer capacity inside that holdout. Architecture search then cannot reuse the same facts used to score the model.