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lib/trends_FIR/hma/Hma.md
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# HMA: Hull Moving Average
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Trend (FIR MA) |
| **Inputs** | Source (close) |
| **Parameters** | `period` |
| **Outputs** | Single series (Hma) |
| **Output range** | Tracks input |
| **Warmup** | `period + sqrtPeriod - 1` bars |
### TL;DR
- HMA (Hull Moving Average) is a solution to the eternal struggle between smoothness and lag.
- Parameterized by `period`.
- Output range: Tracks input.
- Requires `period + sqrtPeriod - 1` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "Alan Hull looked at the lag in moving averages and said, 'I can fix that.' And he did, by making the math do gymnastics."
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.
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1. **Overshoot**: Like DEMA, HMA can overshoot price turns because of the lag correction.
2. **Period Sensitivity**: The $\sqrt{N}$ smoothing is hardcoded into the definition. You can't easily tweak the smoothing independently of the lag correction without breaking the "Hull" definition.
3. **Integer Math**: The periods $N/2$ and $\sqrt{N}$ are rounded to integers. This can cause slight discrepancies between implementations depending on rounding rules. Standard integer truncation is used in QuanTAlib.
3. **Integer Math**: The periods $N/2$ and $\sqrt{N}$ are rounded to integers. This can cause slight discrepancies between implementations depending on rounding rules. Standard integer truncation is used in QuanTAlib.