Bezier-curve price trend filter

Control vertices along a fixed lookback

A bezier-curve is a cubic spline whose path is determined by a small set of control vertices and cannot cross itself. Each control-vertex is an ordered pair of sampling distance and price that pins the spline. The newest observation sits at the far end of a fixed lookback, and earlier prices sit at earlier distances.

The demonstration construction used seven vertices sampled at 28, 23, 18, 13, 8, 5 and 0 periods back, with the newest price as the last control point.

Weighted blending and output resolution

Each point on the finished curve is a weighted blend of all control vertices. The path begins bending toward later vertices immediately and is pulled off a straight line between the first two points.

Output resolution is a separate parameter. The demonstration spline was assembled from 30 line segments. Finer segmentation increases computation without changing the vertex set.

Using every price as a control vertex collapses the spline into a connect-the-dots plot. Too many vertices therefore fail to filter noise, because more vertices make the curve hug raw prices more closely.

Comparing the close with one segment-value

A trend-filter damps noisy price movement and compares the latest close with a smoothed baseline at a defined lookback. The archive workflow uses a rudimentary trading filter that compares the current close with one chosen segment. That segment-value is the comparison level for a long or short bias. A close above the segment is treated as an upside breakout-bias, and a close below it as a downside breakout-bias.

Early segments lag recent prices and late segments chase them, so the chosen segment index sets responsiveness in the same way a moving-average length does.

The same spline construction was applied to daily series and to half-hour series, with the close compared against segment indices 2, 7, 12, 17 and 22.