Miha Kralj
a7b7207801
- Updated mathematical foundations and performance profiles where necessary to maintain clarity and coherence.
2.4 KiB
DEMA: Double Exponential Moving Average
"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.
Historical Context
Introduced by Patrick Mulloy in the January 1994 issue of Technical Analysis of Stocks & Commodities, DEMA was designed to reduce the lag of trend-following indicators. Mulloy realized that smoothing always introduces lag, but by combining single and double smoothing, you could mathematically negate some of that delay.
Architecture & Physics
DEMA is a composite indicator built from two EMAs.
- EMA1: The standard EMA of the price.
- EMA2: The EMA of EMA1.
The "physics" relies on the fact that EMA2 lags EMA1 roughly as much as EMA1 lags the price. Therefore, 2 \times \text{EMA1} - \text{EMA2} pushes the value forward, correcting the lag.
Mathematical Foundation
\text{EMA}_1 = \text{EMA}(P, N)
\text{EMA}_2 = \text{EMA}(\text{EMA}_1, N)
\text{DEMA} = 2 \times \text{EMA}_1 - \text{EMA}_2
Where N is the period.
Performance Profile
DEMA is extremely fast, requiring only a few floating-point operations per update.
| Metric | Complexity | Notes |
|---|---|---|
| Throughput | Extreme | 2x EMA cost (still O(1)) |
| Complexity | O(1) | Recursive calculation |
| Accuracy | 7/10 | Good for trends, but can be erratic |
| Timeliness | 9/10 | Very fast, minimal lag |
| Overshoot | 4/10 | Prone to overshoot on reversals |
| Smoothness | 5/10 | Can be jagged due to speed |
Validation
Validated against TA-Lib and Skender.Stock.Indicators.
| Provider | Error Tolerance | Notes |
|---|---|---|
| TA-Lib | 10^{-9} |
Matches TA_DEMA |
| Skender | 10^{-9} |
Matches GetDema |
Common Pitfalls
- Overshoot: Because DEMA subtracts lag, it can sometimes overshoot price turns. It's more volatile than a standard EMA.
- "Double" Misconception: It is not a moving average of a moving average (that would be slower). It is a lag-corrected composite.
- Warmup: DEMA needs about
2 \times Nbars to converge fully, as the second EMA needs the first EMA to stabilize.