doc headers

lib/trends_IIR/dema/Dema.md

@@ -1,5 +1,22 @@
 # DEMA: Double Exponential Moving Average
 
+| Property         | Value                            |
+| ---------------- | -------------------------------- |
+| **Category**     | Trend (IIR MA)                        |
+| **Inputs**       | Source (close)                          |
+| **Parameters**   | `period`                      |
+| **Outputs**      | Single series (Dema)                       |
+| **Output range** | Tracks input                     |
+| **Warmup**       | `period` bars                          |
+
+### TL;DR
+
+- DEMA (Double Exponential Moving Average) is not just "two EMAs." It's a clever mathematical hack to cancel out the lag inherent in a standard EMA.
+- Parameterized by `period`.
+- Output range: Tracks input.
+- Requires `period` bars of warmup before first valid output (IsHot = true).
+- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
+
 > "EMA is good. DEMA is better. It's like an EMA that drank a double espresso and stopped lagging behind the conversation."
 
 DEMA (Double Exponential Moving Average) is not just "two EMAs." It's a clever mathematical hack to cancel out the lag inherent in a standard EMA. By subtracting the "error" (the difference between a single EMA and a double EMA) from the original EMA, DEMA produces a curve that hugs the price action much tighter. The extrapolation formula $2 \times \text{EMA}_1 - \text{EMA}_2$ effectively predicts where EMA "should be" based on its current trajectory.
@@ -235,4 +252,4 @@ Both EMA states are rolled back atomically for consistent correction.
 
 ## References
 
-- Mulloy, P. (1994). "Smoothing Data with Faster Moving Averages." *Technical Analysis of Stocks & Commodities*, 12(1), 11-19.
+- Mulloy, P. (1994). "Smoothing Data with Faster Moving Averages." *Technical Analysis of Stocks & Commodities*, 12(1), 11-19.