- **Similar:** [DEMA](../../trends_IIR/dema/dema.md), [TEMA](../../trends_IIR/tema/tema.md) | **Complementary:** Signal line crossover | **Trading note:** Alan Hulls MA; cascades WMAs to nearly eliminate lag while maintaining smoothness.
HMA (Hull Moving Average) is a solution to the eternal struggle between smoothness and lag. Most indicators force you to choose one; HMA gives you both. It achieves this by using weighted moving averages (WMAs) in a clever configuration that cancels out lag while maintaining the smoothing properties of the WMA.
## Historical Context
Developed by Alan Hull in 2005, the HMA was designed to be "responsive, accurate, and smooth." Hull realized that lag is essentially a function of the period, and by combining averages of different periods (specifically, a full period and a half period), he could mathematically offset the lag.
## Architecture & Physics
The HMA is built from three Weighted Moving Averages (WMAs):
1.**WMA(n/2)**: A fast WMA of half the period.
2.**WMA(n)**: A slow WMA of the full period.
3.**WMA(sqrt(n))**: A smoothing WMA applied to the difference.
The core logic is: $2 \times \text{WMA}(n/2) - \text{WMA}(n)$.
This operation "over-weights" the recent data, pushing the average forward to align with the current price. The final WMA smooths out the resulting noise.
This results in different effective periods for $N=14$ ($\sqrt{14} \approx 3.74 \to 3$ vs $4$) and others where the fractional part $\ge 0.5$. Validation tests match exactly for periods where rounding logic aligns (e.g., $N=9, 20, 50$).
