Constructing calibrated market-breadth summation indexes

Breadth as a restatement problem

Editorial reading: market breadth can be taught as a restatement problem. One net-advance residual is rebuilt in several ways, and each rebuild is a different horizon hypothesis rather than a new market fact.

The archive starts from that shared residual and then constructs a cumulative line, a two-speed gap, a running sum of that gap, and a zero-anchored recombination of the same two smoothers.

The shared net-advance residual

A net-advance series is formed by pairing advancing-issue counts with declining-issue counts and subtracting the declining series from the advancing series. That daily difference is the net-advance residual used as the shared raw input.

Later constructions in this workflow restate that residual. The archive does not introduce a second breadth series.

A cumulative line, a two-speed gap, and a summation

The advance-decline line is constructed as the cumulative sum of the net-advance residual. It is a running total of the same daily difference.

One oscillator construction subtracts a 39-period exponential moving average of the net-advance residual from a 19-period exponential moving average of the same residual. That gap is the two-speed oscillator.

An equivalent recursive construction updates two smoothers of the same advancing-minus-declining residual with constants 0.1 and 0.05, then subtracts the slower smoother from the faster smoother.

The summation index is constructed as the cumulative sum of that oscillator.

A calibrated recombination on a fixed scale

The calibrated summation index is defined as 1000 minus 9 times the 19-period exponential average plus 19 times the 39-period exponential average of the net-advance residual.

The same two recursive smoothers can be recombined as 1000 minus 9 times the 0.1 smoother plus 19 times the 0.05 smoother to produce that calibrated index.

Editorial reading: the calibration recenters the long-horizon reading on a fixed numeric scale so a later chart rule can use a zero line rather than a drifting cumulative level.

The zero-line convention

The archive treats the long-horizon breadth state as up when the calibrated summation index remains above zero.

It also treats a recent move of the summation index through zero as a negative long-horizon breadth reading.

Under the zero-line convention, the sign of the calibrated index, not a price level, is the long-horizon breadth state.