Constructing forecast inputs with moving averages, Fourier transforms and intermarket spreads

Construction is the input object

A price-forecast construction is described as incomplete unless it combines the target market's own technical series with related-market series and fundamentals that affect that market. Transformation in this workflow is the rewriting of one or more raw series into a single model input that highlights a chosen feature such as change, smooth, spread or regime.

Noise cuts on the target series

A moving average is a lookback smoother of ordered price, volume or breadth that can be supplied as a constructed input so a forecast model sees less bar-to-bar noise. A five-day simple moving average of the close is offered as a transform for a next-close forecast because it supplies a coarser signal and reduces noise. The same construction notes that smoothing can also discard useful detail.

Fast Fourier Transform is a spectral transform used as an advanced noise-reduction step on an ordered market series before training. It is listed among advanced noise-reduction transforms for the target-market series, alongside simple or exponential moving averages and other smoothing.

Related-market series and spreads

Intermarket analysis here means construction of related-market series and spreads so a single-market forecast is conditioned on cross-market structure rather than isolated prices. Related-market construction for a next-day Treasury-bond high and low is illustrated with a dollar-index series, an equity-index series and a German government-bond series, chosen with domain knowledge and correlation checks against the target.

Spreads between the target series and related-market series are recommended so cross-market relationships become explicit inputs rather than raw parallel price levels.

Matching fundamentals and compact transforms

Fundamentals should be sampled or aggregated on a horizon that matches the target. Daily or at least weekly series are used for a next-day high. Weekly or monthly series are used for a weekly target. Daily bars may be collapsed by average, maximum or minimum.

Differences and ratios are listed as simple transforms that cut the input count. State classifiers such as directional or overbought-oversold measures are suggested so the same observation can be read differently in advancing, declining or range-bound conditions.

Normalization and a reversible output scale

Normalization is the scaling of each constructed input and output into the neuron range, optionally after clipping, with the same rule applied in training and later use.

Linear scaling maps each input from its sample minimum and maximum onto the neuron range, commonly -1 to 1 or 0 to 1, using I = Imin + (Imax - Imin)(D - Dmin)/(Dmax - Dmin). That linear map does not change the shape of the frequency distribution.

A second scaling sets bounds at the mean minus and plus a chosen number of standard deviations. For a mean of 50, a standard deviation of 3 and two deviations, the lower bound is 44. Values outside those bounds are clipped, then the linear map is applied so the distribution spreads and becomes more uniform.

A reversible output scale is required: the output transform can be inverted, and values sitting on a clip bound must be read as censored rather than exact. When training outputs were clipped, a later output sitting on a clip bound is to be read as at or beyond that bound, so the output transform must be reversible enough for the forecast use case.