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lib/trends_IIR/hema/Hema.md
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# HEMA: Hull Exponential Moving Average
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Trend (IIR MA) |
| **Inputs** | Source (close) |
| **Parameters** | `period` |
| **Outputs** | Single series (Hema) |
| **Output range** | Tracks input |
| **Warmup** | `EstimateWarmupPeriod()` bars |
### TL;DR
- HEMA is a Hull-style moving average built entirely from **exponential smoothers**.
- Parameterized by `period`.
- Output range: Tracks input.
- Requires `EstimateWarmupPeriod()` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "HMA is a topology. HEMA keeps the topology and swaps the physics: windows to decay, with identical lag."
## An EMA-domain analog of HMA with WMA-lag-matched alphas
> "HMA is a topology. HEMA keeps the topology and swaps the physics: windows to decay, with identical lag."
HEMA is a Hull-style moving average built entirely from **exponential smoothers**. It preserves the classic HMA pipeline (fast minus slow, then smooth) but replaces WMA sub-filters with EMAs whose alphas are tuned to produce **identical lag** to the WMA stages they replace. At period $N$: HEMA($N$) and HMA($N$) have the same theoretical group delay, but HEMA has infinite memory and smoother transient behavior.