Constructing MACD from exponential-average spreads for crossover and divergence

Three layers of MACD

MACD is an oscillator built as the gap between a shorter and a longer exponential average of price, plotted around a horizontal equilibrium. The fast line is the raw MACD value, equal to the shorter exponential average minus the longer one. The signal line is an exponential average of the fast line that serves as the crossover partner. The MACD histogram is the bar series of the residual between the fast line and the signal line, used to watch slope before a line-form event.

Lookbacks and the smoothing constant

The fast line is a shorter exponential average of price minus a longer one, with 12-period and 26-period lengths presented as the usual pair. The signal line is a nine-period exponential average of that fast line. The lookbacks used to form one side of a moving-average-crossover reading may differ from those used on the other side.

Each exponential average is seeded with a simple mean over its lookback, then updated with the smoothing constant. That weight is 2/(n+1) on the newest price, with the complement applied to the prior average. The 12-, 26-, and 9-period weights shown are 0.154, 0.074, and 0.2.

Histogram residual and slope

The histogram is the residual of fast line minus signal line, drawn as bars around the zero line so bar height tracks how far the two averages have separated. The zero line is the equilibrium of the oscillator. Histogram bars that shrink after an extreme are treated as an earlier momentum-fade cue than waiting for the line form to recross the zero line.

Moving-average crossover and the zero line

A moving-average crossover is the condition in which the fast line crosses the signal line, optionally filtered by distance from the zero line. A long-side reading is defined when the fast line crosses above the signal line, and a short-side reading when it crosses below. A cross near the zero line is treated as a stronger directional setup than a cross far from it. Where a crossover sits relative to the zero line is part of the signal rule.

Divergence as an unconfirmed extreme

Divergence is a mismatch in which price makes a new extreme that the oscillator does not confirm. That mismatch is treated as a delayed reversal hypothesis that can print false readings before price turns.

Range, stretch, and one-way markets

When price stays in a range, the oscillator is used to mark pivot and stretched-move conditions around zero. Overbought-oversold means extreme distance of the oscillator from zero, treated as a stretched-move reading rather than a standalone entry. In a persistent one-way move the two lines can flatten and hug each other, which is given as a reason not to lean on the same crossovers or divergences.

Timing and confirmation charts

A shorter chart is assigned the timing role and a longer chart the confirmation role when both periodicities agree on direction.