Walk-forward optimization of regression-slope-angle rules

Slope angles from selected price segments

A linear fit can be laid through selected parts of a price series so that each segment is summarized as a regression-slope-angle that later rules can read.

Each fit is defined by a segment-length, which is how many bars the line covers, and a start-lag, which is how many bars before the current bar the fitted segment begins.

Joint search of length, lag, gates, and quorum

A genetic search can jointly choose how many such segments to place, each segment-length, each start-lag, and the angle gates used as conditions. The search maximizes an objective-score, such as profit or another stated function, while it assembles the procedure.

A long condition can require that a fitted segment of chosen segment-length, starting at a chosen start-lag, has a regression-slope-angle steeper than a chosen angle. The same search also chooses the rule-quorum, which is how many of those slope-versus-angle conditions must hold before a long order is allowed.

The search may place overlapping-segments that share bars. That overlap is treated as an intended design choice, so nearby geometries can vote together.

Long and short as one reversal-procedure

Short conditions use the complementary test of a regression-slope-angle falling below an angle. Long and short conditions can be fitted together as one reversal-procedure for a single instrument and period, so the book is always considering a flip rather than two independent one-way systems.

The unused-window as the designated test

Parameter search is confined to an in-sample-window, the earlier stretch used only to choose segment counts, segment-length values, start-lag values, angles, and rule-quorum. The frozen rules are then evaluated on a later unused-window.

That later walk-forward check is the designated test of whether the procedure generalizes. Both the in-sample-window and the unused-window were scored against a buy-and-hold baseline.

A slope-only demonstration and later variants

The worked example used only slope-versus-threshold rules and did not insert a neural network. The same optimized slopes can later become inputs to a predictive network. The demonstration applied the slope-rule procedure to a 30-minute price series.

Design variants include adding opposite-side threshold tests, requiring a regression-slope-angle to lie between two angles, and allowing the search to relax other variables when some search ranges are set too tightly.