Constructing head-and-shoulders milestone points

A poor tool for a scale-free shape

A simple percentage-swing connector is a poor construction tool for head-and-shoulders because real charts produce many zigzag variants of the same textbook shape. Classic chart formations are treated as scale-free. They may span a few bars or hundreds, and their swings may be tiny or large, so a fixed swing threshold is inefficient.

What the construction is designed to do

The construction is designed to stay scale-free, use as few parameters as possible, cover many head-and-shoulders variants without becoming too loose, and ignore price action outside the formation. The procedure is meant to mark completed closing-price head-and-shoulders structures after the close has already pierced the neckline, and to do so in uptrends, sideways markets, and downtrends.

This article only prepares the milestone-points that a later neckline-penetration test will use.

Start with two parameters

Two parameters start the high search. The n-window, with default 5, is the recent-bar lookback used to find the lowest close X that starts the head search. The factor, with default 1, is the left-to-right duration multiplier that sets how far left of the head the search for the left shoulder may travel. It scales the left-half duration from the right-half bar count between the head and X.

That pairing is a scale-free-construction. It locates the points from relative bar distances and local extremes so the same steps can apply from a few bars to a long formation.

Mark the head and the left-half anchor

The head H is the highest close between the first leftward close B that is at or below X and the recent low X. D is then the close Lhalf bars before H.

Locate the shoulder highs

Temporary lows in the rightmost two-thirds of D-to-H and the leftmost two-thirds of H-to-X locate shoulder highs. H1 is the highest close from D to tL1, and H2 is the highest close from tL2 to X.

Close the skeleton with inner and outer lows

Inner lows are built from local troughs and fractional averages. L1 is the first leftward close at or below (tL1 + 2E)/3, and L2 is the first leftward close at or below (tL2 + F)/2. Outer lows close the skeleton. L0 is the first leftward close at or below L1 plus one-fifth of the H1-to-L1 range, and L3 is the first leftward close from the last bar that is at or below L2.

These labeled closing-price highs and lows, H, H1, H2, L0, L1, L2, and L3, are the milestone-points. A recognition procedure must first define them before any pattern test can run. In this usage, a head-and-shoulders is a five-peak closing-price structure whose left shoulder, head, and right shoulder are located from those named milestone highs and lows rather than from a visual sketch.

Points first, pattern later

These milestone-points can be drawn even when no head-and-shoulders is present. They also need not be the most prominent local highs and lows, so a later condition set is required before the points outline a pattern.