Constructing supervised forecasts on moving averages

Why a trainable map

When many paired examples exist but the mapping from ordered market observations to a target is poorly specified, a trainable network is offered as a pattern-recognition and noise-filtering alternative to an explicit algorithm. The same construction is described as a way to model ordered financial series and to emit a plotted forecast from a sample simulator.

The construction is described as adaptive and massively parallel, with inputs and outputs cross-compared for relationships, and as trained on data rather than written as fixed program rules.

From a moving average to a processing element

The equal-weight moving average of the last N prices becomes a weighted moving average when each 1/N coefficient is replaced by its own weight. That weighted sum is treated as the fully connected input stage of one processing element.

A transfer function is applied to that weighted sum. A sigmoid form is used as a soft-saturating map onto the unit interval, returning the asymptotic bounds when the raw input would overflow.

Supervised learning on a fixed window

Supervised training for a five-period-ahead price target uses a ten-input window. With thirty periods of history indexed so the latest bar is zero, inputs P(-29) through P(-20) are corrected against the later observed price P(-15).

Weight correction may use a Hebbian threshold update, a least-mean-square rule that multiplies a signal error by a learning-rate factor and optional momentum, or a generalized delta rule that assigns a share of that error to earlier layers.

An untrained baseline on the same task

The trained pattern-recognition forecast is constructed to be checked against explicit moving-average baselines on the same weekly close-to-close trend task, including four-week and ten-week averages.