Exponential Moving Average (EMA)

Measures: a moving average that weights recent bars more heavily, reacting faster than the SMA.

Formula:

k       = 2 / (n + 1)                      (smoothing factor)
EMA_t   = C_t × k + EMA_(t−1) × (1 − k)
EMA_0   = C_0                              (seed)

Calculation: seeded with the first close, then recursively blended. Because the seed biases early values, the engine requires at least 5×n bars of history before any EMA-derived signal is trusted, which the lookback windows in the design doc guarantee.

Parameters: n = 12 and 26 — used exclusively as MACD inputs. The engine never reads EMAs directly.

Limitations: faster reaction also means more false signals in chop. This is contained by feeding EMAs only into MACD, whose reading is in turn discounted by the ADX quality multiplier at the family level.

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