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Add new moving average implementations: LTMA, MCNMA, NLMA, NMA, NYQMA, RAIN, and TRAMA

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- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation.
- MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness.
- NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages.
- NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel.
- NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages.
- RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing.
- TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
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> "The Impulse System identifies inflection points where a trend speeds up or slows down." -- Alexander Elder, *Come Into My Trading Room*
The Elder Impulse System combines a 13-period exponential moving average (trend inertia) with the MACD(12,26,9) histogram (momentum) to classify each price bar into one of three states: bullish, bearish, or neutral. It is the rare indicator that answers "should I be trading this direction right now?" with a single color.
The Elder Impulse System combines a 13-period EMA (trend inertia) with the MACD(12,26,9) histogram (momentum acceleration) to classify each bar as bullish (+1), bearish (-1), or neutral (0). Both EMA slope and histogram slope must agree for a directional signal; disagreement forces neutral. The system functions as a permission filter rather than a signal generator, requiring 34 bars warmup and running at O(1) per bar through composition of two child indicators.
## Historical Context
Alexander Elder introduced the Impulse System in his 2002 book *Come Into My Trading Room*. Elder, a psychiatrist turned trader, designed it as a censorship system: green bars permit long entries, red bars permit short entries, and blue bars prohibit new positions in either direction. The system enforces discipline by requiring both trend and momentum to align before committing capital.
Alexander Elder introduced the Impulse System in *Come Into My Trading Room* (2002). A psychiatrist turned trader, Elder designed it as a discipline enforcement mechanism: green bars permit long entries, red bars permit short entries, blue bars prohibit new positions in either direction. The intellectual lineage runs through Gerald Appel's MACD (1979) and Thomas Aspray's MACD Histogram (1986). Elder's contribution was combining first-derivative (EMA slope) and second-derivative (histogram slope) filters into a single ternary decision gate. Most implementations treat this as a visual color overlay; QuanTAlib exposes it as a programmatic discrete signal for algorithmic consumption.
The intellectual lineage runs through Gerald Appel's MACD (1979), which separated trend from momentum, and Thomas Aspray's MACD Histogram (1986), which revealed the rate of change within the MACD itself. Elder's contribution was recognizing that combining EMA slope (inertia proxy) with histogram slope (momentum proxy) produces a decision filter superior to either component alone.
## Architecture & Physics
Most implementations treat this as a visual overlay with colored bars. QuanTAlib exposes it as a programmatic signal (+1, 0, -1) for algorithmic consumption, while the Quantower adapter provides the traditional color-coded visualization.
### 1. EMA Component (Trend Inertia)
## Architecture
### Component Composition
The Impulse indicator composes two child indicators internally:
1. **EMA(13)** on close price: measures trend inertia via exponential smoothing
2. **MACD(12,26,9)**: provides the histogram (MACD Line minus Signal Line) for momentum measurement
Both child indicators manage their own state, warmup compensation, and bar correction. The Impulse class tracks only the previous EMA value and previous histogram value for slope comparison.
### Signal Classification
```text
EMA_slope = sign(EMA_current - EMA_previous)
Hist_slope = sign(Histogram_current - Histogram_previous)
Signal = +1 (Green/Bullish): EMA_slope > 0 AND Hist_slope > 0
Signal = -1 (Red/Bearish): EMA_slope < 0 AND Hist_slope < 0
Signal = 0 (Blue/Neutral): otherwise
```
The neutral state fires whenever the two components disagree. This is the system's core value proposition: it identifies transition zones where conviction is insufficient for new entries.
## Mathematical Foundation
### EMA Component
The 13-period EMA uses the standard recursive formulation:
The 13-period EMA tracks trend direction via exponential smoothing:
$$\alpha = \frac{2}{n + 1} = \frac{2}{14} \approx 0.1429$$
$$\text{EMA}_t = \alpha \cdot \text{Close}_t + (1 - \alpha) \cdot \text{EMA}_{t-1}$$
QuanTAlib's EMA implementation includes warmup bias compensation:
With warmup bias compensation:
$$\text{EMA}_{\text{corrected}} = \frac{\text{EMA}_{\text{raw}}}{1 - (1-\alpha)^n}$$
$$\text{EMA}_{\text{corrected}} = \frac{\text{EMA}_{\text{raw}}}{1 - (1 - \alpha)^t}$$
### MACD Histogram Component
The EMA slope $\Delta_{\text{EMA}} = \text{sign}(\text{EMA}_t - \text{EMA}_{t-1})$ represents smoothed trend direction (first derivative of price).
### 2. MACD Histogram Component (Momentum Acceleration)
$$\text{MACD Line} = \text{EMA}(12) - \text{EMA}(26)$$
$$\text{Signal Line} = \text{EMA}(9, \text{MACD Line})$$
$$\text{Signal} = \text{EMA}(9,\ \text{MACD Line})$$
$$\text{Histogram} = \text{MACD Line} - \text{Signal Line}$$
$$\text{Histogram} = \text{MACD Line} - \text{Signal}$$
The histogram is the second derivative of price (acceleration), making the Impulse System a combined first-derivative (EMA slope) and second-derivative (histogram slope) filter.
The histogram is the second derivative of price (acceleration). Its slope $\Delta_{\text{Hist}} = \text{sign}(\text{Hist}_t - \text{Hist}_{t-1})$ indicates whether momentum is building or fading.
### Warmup Period
### 3. Signal Classification
$$W = \max(\text{emaPeriod}, \text{macdSlow}) + \text{macdSignal} - 1 = \max(13, 26) + 9 - 1 = 34$$
$$\text{Impulse} = \begin{cases} +1 & \text{if } \Delta_{\text{EMA}} > 0 \text{ and } \Delta_{\text{Hist}} > 0 \\ -1 & \text{if } \Delta_{\text{EMA}} < 0 \text{ and } \Delta_{\text{Hist}} < 0 \\ 0 & \text{otherwise} \end{cases}$$
The indicator requires 34 bars before producing valid signals. IsHot becomes true when both child indicators are warmed up and at least two comparison values exist.
The neutral state fires whenever the two components disagree, identifying transition zones where conviction is insufficient for new entries.
## Performance Profile
### 4. Warmup
$$W = \max(13, 26) + 9 - 1 = 34 \text{ bars}$$
Both child indicators must be warmed up and at least two comparison values must exist before valid signals emerge.
### 5. Complexity
| Metric | Value |
| :----- | :---- |
| Update complexity | O(1) per bar |
| Memory | 3 internal EMA states + MACD state + 4 doubles for comparison |
| Allocations in Update | Zero (delegates to child indicator Update methods) |
| SIMD potential | None (serial comparison logic) |
|:-------|:------|
| Time | O(1) per bar (delegates to child EMA/MACD updates) |
| Space | O(1) (3 internal EMA states + 4 doubles for slope comparison) |
| Allocations | Zero in hot path |
### Quality Metrics
## Mathematical Foundation
| Metric | Score (1-10) |
| :----- | :----------- |
| Lag | 4 (moderate; EMA(13) + histogram smoothing introduce delay) |
| Noise rejection | 7 (requires dual confirmation) |
| Signal clarity | 9 (ternary output with no ambiguity) |
| Computational efficiency | 9 (pure O(1) composition) |
| Parameter sensitivity | 6 (Elder's defaults are widely used; customization possible but rarely needed) |
### Parameters
## Validation
| Parameter | Type | Default | Constraint | Description |
|:----------|:-----|:--------|:-----------|:------------|
| emaPeriod | int | 13 | > 0 | EMA period for trend inertia |
| macdFast | int | 12 | > 0 | MACD fast EMA period |
| macdSlow | int | 26 | > macdFast | MACD slow EMA period |
| macdSignal | int | 9 | > 0 | MACD signal smoothing period |
No external libraries (TA-Lib, Skender, Tulip, OoplesFinance) implement the Elder Impulse System as a standalone indicator. Validation uses self-consistency checks:
### Pseudo-code
| Test | Method |
| :--- | :----- |
| EMA identity | Impulse EMA output matches standalone EMA(13) |
| Signal correctness | Manual EMA + MACD comparison produces identical signals |
| Streaming == Batch | Streaming and batch modes produce identical EMA values |
| Determinism | Same input sequence produces identical output |
| Directional | Steady uptrend produces +1; steady downtrend produces -1 |
```
IMPULSE(close, emaPeriod=13, macdFast=12, macdSlow=26, macdSignal=9):
## Interpretation
// Child indicator updates
ema_val = EMA.Update(close, emaPeriod)
macd_result = MACD.Update(close, macdFast, macdSlow, macdSignal)
hist_val = macd_result.Histogram
The Impulse System operates as a **permission filter**, not a signal generator:
// Slope computation (requires previous values)
ema_slope = sign(ema_val - prev_ema)
hist_slope = sign(hist_val - prev_hist)
- **Green (+1):** Both inertia and momentum favor bulls. Long entries permitted; short entries prohibited.
- **Red (-1):** Both inertia and momentum favor bears. Short entries permitted; long entries prohibited.
- **Blue (0):** Disagreement between trend and momentum. No new entries in either direction; existing positions may be held or tightened.
// Classification
if ema_slope > 0 AND hist_slope > 0:
signal = +1 // Bullish: both inertia and momentum rising
else if ema_slope < 0 AND hist_slope < 0:
signal = -1 // Bearish: both inertia and momentum falling
else:
signal = 0 // Neutral: disagreement between components
### Multi-Timeframe Application
// State update
prev_ema = ema_val
prev_hist = hist_val
Elder recommends using the Impulse System across two timeframes (5:1 ratio):
return signal
```
1. Weekly chart: determines the "big picture" trend direction
2. Daily chart: identifies entry points aligned with the weekly trend
### Derivative Interpretation
Trade only when the higher timeframe is not red (for longs) or not green (for shorts).
The system combines two derivatives:
## Common Pitfalls
- **First derivative** (EMA slope): Is the smoothed trend rising or falling?
- **Second derivative** (histogram slope): Is the rate of MACD convergence/divergence accelerating or decelerating?
1. **Using Impulse as an entry signal instead of a filter.** The system identifies when trading is permitted, not when to trade. Combine with entry triggers (pullbacks, breakouts).
Both must confirm for a directional signal. This dual-confirmation suppresses false signals during transitions but introduces lag at inflection points.
2. **Ignoring the neutral state.** Blue bars are not "do nothing" -- they indicate transitions. Watch for the sequence blue-then-green or blue-then-red for early signals.
3. **Overriding the prohibition.** Going long on a red bar or short on a green bar defeats the system's purpose. The whole point is discipline enforcement.
4. **Expecting the system to catch tops and bottoms.** The EMA and histogram lag price. By design, the system trades the middle of moves, not the extremes.
5. **Modifying the default parameters without understanding the impact.** The 13-period EMA and 12/26/9 MACD are Elder's specific design choices. Shorter periods increase noise; longer periods increase lag. The defaults balance both.
6. **Confusing EMA direction with price direction.** Price can close higher while EMA still falls (or vice versa). The EMA slope represents smoothed trend, not raw price movement.
## References
## Resources
- Elder, A. (2002). *Come Into My Trading Room*. John Wiley and Sons.
- Elder, A. (1993). *Trading for a Living*. John Wiley and Sons.
- Appel, G. (1979). "The Moving Average Convergence-Divergence Method."
- Aspray, T. (1986). "MACD Histogram." *Technical Analysis of Stocks and Commodities*.
- StockCharts.com. "Elder Impulse System." ChartSchool.