MACD parameter order and cycle phase lag

Copied lengths assume the same cycle

A conventional MACD construction is often transplanted without asking whether the bar interval still holds the cycle those lengths came from. Lengths of 26 and 13 that originated on weekly stock cycles are frequently copied onto daily commodity bars, which implicitly assumes those same cycle counts exist at the daily sampling interval.

The archive treats markets as changing and therefore treats average lengths as quantities that should be retuned to present conditions instead of held constant.

The macd-line and the signal-line

A conventional macd-line is the shorter exponential average minus the longer one. The signal-line is a third exponential average of that difference, often given the same length as the shorter average to keep the construction simple.

Read the macd-line as a timing residual rather than a price forecast. After very slow trend components have been removed, that difference is a detrended-synthetic-price that sits near the remaining cyclic swing.

exponential-smoothing is a recursive average that blends the latest observation with the previous average. An exponential average updates as yesterday's value plus a smoothing constant times the gap between today's price and that value. The constant is often estimated as 2 divided by one plus the comparable simple-average length.

Cycle-matched-lengths on a counted swing

Between mid-February and late April the archive counted about 12 trading days from high to high or low to low. It then assigned a 12-period first average and a 6-period second average, using that same 6-period length for the signal smoother.

That pairing is cycle-matched-lengths: the slower average near one full measured swing and the faster average near half that swing.

Phase-lag spent by each average

A full-cycle exponential average is described as imposing about 72 degrees of phase-lag and reducing cycle amplitude to about 31 percent. A half-cycle average imposes about 54 degrees and leaves about 57 percent.

Vector subtraction of the longer average from the shorter is said to leave a residual about 35 degrees behind price. The half-cycle signal-line adds about 54 degrees, so the cross occurs near 62 degrees after the crest or trough. On a 12-day cycle that delay is about two days. After a next-bar fill the same construction sits about 90 degrees late, which on a pure cycle implies a theoretical pre-cost break-even if exit is delayed by the same amount.

Inverse-length-order and the parameter-surface

A parameter-surface, a grid of the two exponential-average lengths against a historical outcome metric, was described as relatively smooth. That smoothness implies low local sensitivity to small length changes. The extreme of that surface sat in the region where the first length is shorter than the second, which is inverse-length-order, the opposite of the usual MACD convention.

A 4-and-12 length pair produced marks early relative to cyclic highs and lows. The archive states that pair applies only to the immediate past of the illustrated window and generated a contrary January mark.

On a 12-day cycle, a 4-period average is described as retaining about 80 percent of amplitude with about 40 degrees of lag, and a 12-period average as retaining about 31 percent with about 72 degrees. Inverting the shorter vector yields a MACD about 203 degrees behind price, or 157 degrees ahead of the next cycle. After a further 72-degree signal delay the crosses lead the next cycle by about 67 degrees.

Retire the pair when the swing changes

The archive workflow measures a swing, assigns lengths, and does not treat those lengths as permanent. Editorial reading: once the counted cycle changes, the phase budget changes with it, so the pair should be retired rather than copied forward.