MACD

Definition

MACD (moving average convergence/divergence, Gerald Appel’s construction) is the difference between a fast and a slow EMA, plus a signal line (an EMA of that difference) and a histogram (the gap between the two). It restates EMA-crossover logic as an oscillating momentum measure: MACD above zero means the fast EMA is above the slow (uptrend by that definition); crossings of the signal line mark momentum shifts earlier — and noisier — than zero-line crossings.

How it works / structure

• Formula: MACD = EMA(12) − EMA(26); signal = EMA(9) of MACD; histogram = MACD − signal (12/26/9 are Appel’s defaults — conventions, not constants).
• Parameters (engine-executable): the three windows, price input, and which event is the signal — zero-line cross (slow, trend-confirming), signal-line cross (faster, noisier), histogram sign/slope, or divergence vs price (price makes a new extreme, MACD does not — the divergence convention).
• Nature: MACD is unbounded and scale-dependent (a $500 stock’s MACD dwarfs a $5 stock’s) — cross-instrument comparisons require normalization (divide by price or use indicator-roc).

When it applies

Single-instrument momentum-state tracking where EMA-crossover logic is wanted with a visual momentum-of-momentum layer (histogram); divergence scanning as a hypothesis generator (a weakening-trend flag to investigate, never a standalone signal).

Risk profile & failure modes

• Triple-parameter overfitting: three windows and four signal conventions make MACD a search space, not an indicator — replay-fitted MACD settings are the textbook multiple- testing hazard (lens-quantitative).
• Range whipsaw: inherited from its EMA parents, amplified by the faster signal-line convention.
• Divergence subjectivity: divergences are identified loosely in practice; the engine requires a pinned mechanical definition (extremum windows, minimum separation) or the claim is unfalsifiable.
• Scale illusion: unnormalized MACD magnitudes across instruments or across a stock’s own price history mislead.

Evidence & limits

MACD-specific academic evidence is thin; it enters the tested families of the surveyed literature (Park-Irwin 2007: mixed results, snooping-fragile) as an MA-derivative. Its information content is EMA-crossover content restated; no published study establishes standalone MACD profitability after costs. Divergence lore is folklore until mechanically defined and replayed.

Falsifiable-thesis examples

Illustrations only, not signals:

• “X’s MACD zero-line upcross this week will be followed by a positive 20-session return” — falsified at the mark.
• “Mechanically-defined MACD divergences on universe U precede negative 10-session returns more often than chance this year in replay” — falsified by the tally.

Cross-references

• Parents: indicator-ema; normalized alternative: indicator-roc
• The effect underneath: strategy-momentum
• Method discipline: lens-technical, lens-quantitative