Constructing a two-speed advance-decline oscillator and a calibrated summation

One residual and two clocks

The same two-speed smoothing of a first difference can be applied to momentum in price, volume, or advance-decline counts. The most common illustrated use is a major listing's daily advancing and declining totals.

Market-breadth is the daily imbalance between advancing and declining listings, used as the raw residual that later smoothers consume. Each session's advancing count minus the declining count is the advance-decline residual.

Building the two-speed oscillator

A market-breadth oscillator is built by taking each day's advancing-minus-declining count, smoothing that residual with two exponential moving averages, and subtracting the slower smooth from the faster one. That arithmetic gap is the two-speed oscillator.

The faster exponential trend uses a smoothing constant of 0.1. The slower exponential trend uses a smoothing constant of 0.05.

Exponential-smoothing is a recursive update that blends the latest residual with the prior smooth using a fixed constant such as 0.1 or 0.05. Here those averages are moving-average trends of the same advance-decline residual.

Seeding and updating the trends

Each exponential series is seeded with the first day's raw advance-decline difference, then updated as the prior value plus the smoothing constant times the latest residual minus the prior value.

The illustrated worksheet delayed the calibrated summation until after 28 observations. The accompanying note states the oscillator should be computed for at least 40 periods.

Two ways to start the summation

An unadjusted summation of the oscillator is a simple running total. When that total starts at zero, the illustrated series remained below zero for the entire plotted window.

A calibrated seed of 1000 minus 9 times the 0.1 trend plus 19 times the 0.05 trend places a designated neutral level at 1000 before later oscillator readings are added. That opening value is the neutral-level seed: an initial summation value computed from the two trends so a chosen midpoint sits at the intended center of the scale.

After that seed is set, each later summation value equals the prior calibrated value plus that day's oscillator reading.

With the 1000-neutral calibration applied, the illustrated summation stayed above zero until late in the same sample that the zero-started total never left negative territory.