gavindiaz/QuanTAlib
1
0
Fork 0
mirror of https://github.com/mihakralj/QuanTAlib.git synced 2026-08-25 05:48:06 +00:00
Code Issues Packages Projects Releases Wiki Activity

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

Browse Source 
- 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.
This commit is contained in:
Miha Kralj
2026-02-20 21:40:32 -08:00
parent cbeefc9d64
commit 90d5638008
121 changed files with 9595 additions and 6315 deletions
Download Patch File Download Diff File Expand all files Collapse all files
lib/dynamics/ttm_trend/TtmTrend.md
+68 -83
View File
@@ -1,113 +1,98 @@
# TTM_TREND: TTM Trend Indicator
# TTM_TREND: TTM Trend
> John Carter's TTM Trend - A fast EMA-based trend indicator with color-coded direction.
> "The simplest trend indicator is the one you actually follow."
John Carter's TTM Trend uses a fast EMA (default period 6) applied to typical price (HLC/3) to determine short-term trend direction via slope sign. Output is a ternary trend state: +1 (bullish, EMA rising), -1 (bearish, EMA falling), or 0 (neutral, EMA unchanged). The indicator requires only 2 bars warmup, runs at O(1) per bar with O(1) space, and produces zero allocations in the hot path.
## Historical Context
John Carter developed the TTM (Trade the Markets) Trend indicator as a clean visual tool for identifying short-term trend direction. Popularized through his book *Mastering the Trade* and the thinkorswim platform, it provides a simple but effective way to see trend changes at a glance using color-coded lines.
John Carter developed the TTM (Trade the Markets) Trend indicator as a clean visual tool for identifying short-term trend direction, popularized through *Mastering the Trade* and the thinkorswim platform. Unlike complex multi-component trend systems, TTM Trend reduces trend detection to its minimum viable form: the slope of a fast exponential moving average. The very short default period (6) makes it responsive to recent price action, positioning it as a "first responder" trend filter meant to be combined with Carter's other TTM tools (Squeeze, Wave, LRC). The color-coded output (green/red/gray) provides at-a-glance trend assessment.
## Algorithm
## Architecture & Physics
### Core Calculation
```
alpha = 2 / (period + 1)
EMA = alpha × source + (1 - alpha) × prevEMA
```
### 1. Typical Price
Or equivalently:
```
EMA = alpha × (source - EMA) + EMA
```
$$\text{TP}_t = \frac{H_t + L_t + C_t}{3}$$
### Trend Detection
```
trend = sign(EMA - prevEMA)
+1 = bullish (EMA rising)
-1 = bearish (EMA falling)
0 = neutral (EMA unchanged)
```
Using typical price rather than close reduces susceptibility to closing-tick noise.
### Strength Measurement
```
strength = |EMA - prevEMA| / prevEMA × 100%
```
### 2. EMA Recursion
## Default Parameters
$$\alpha = \frac{2}{N + 1}$$
| Parameter | Value | Description |
|:----------|:------|:------------|
| Period | 6 | EMA lookback period (very fast) |
| Source | HLC/3 | Typical price (High + Low + Close) / 3 |
$$\text{EMA}_t = \alpha \cdot \text{TP}_t + (1 - \alpha) \cdot \text{EMA}_{t-1}$$
## Outputs
Or equivalently via FMA:
| Output | Type | Description |
|:-------|:-----|:------------|
| Value | double | Current EMA value |
| Trend | int | Trend direction: +1, -1, or 0 |
| Strength | double | Percent change between EMA values |
| IsHot | bool | True after warming up (2 bars) |
$$\text{EMA}_t = \text{FMA}(\alpha,\ \text{TP}_t - \text{EMA}_{t-1},\ \text{EMA}_{t-1})$$
## Color Coding
### 3. Trend Classification
| Color | Condition | Meaning |
|:------|:----------|:--------|
| 🟢 Green | Trend > 0 | EMA rising (bullish) |
| 🔴 Red | Trend < 0 | EMA falling (bearish) |
| ⚫ Gray | Trend = 0 | EMA unchanged (neutral) |
$$\text{Trend}_t = \text{sign}(\text{EMA}_t - \text{EMA}_{t-1})$$
## Performance
| Value | State | Color |
|:------|:------|:------|
| +1 | Bullish | Green |
| -1 | Bearish | Red |
| 0 | Neutral | Gray |
### 4. Strength Measurement
$$\text{Strength}_t = \frac{|\text{EMA}_t - \text{EMA}_{t-1}|}{\text{EMA}_{t-1}} \times 100\%$$
This percentage rate-of-change quantifies how aggressively the trend is moving. High strength values indicate strong conviction; near-zero values suggest potential reversal.
### 5. Complexity
| Metric | Value |
|:-------|:------|
| Time complexity | O(1) per bar |
| Space complexity | O(1) |
| Warmup period | 2 bars |
| Time | O(1) per bar |
| Space | O(1) (one EMA state + one previous value) |
| Warmup | 2 bars |
| Allocations | Zero in hot path |
## Usage Examples
## Mathematical Foundation
### Basic Usage
```csharp
var ttm = new TtmTrend(period: 6);
### Parameters
// Update with typical price
var result = ttm.Update(new TValue(time, typicalPrice));
| Parameter | Type | Default | Constraint | Description |
|:----------|:-----|:--------|:-----------|:------------|
| period | int | 6 | > 0 | EMA lookback period (very fast by default) |
// Or update with bar (uses HLC/3 automatically)
var result = ttm.Update(bar);
### Pseudo-code
// Access trend direction
if (ttm.Trend > 0) { /* bullish */ }
else if (ttm.Trend < 0) { /* bearish */ }
```
TTM_TREND(bar, period=6):
tp = (bar.High + bar.Low + bar.Close) / 3
alpha = 2.0 / (period + 1)
if count == 0:
ema_val = tp
else:
ema_val = FMA(alpha, tp - ema_val, ema_val)
// Trend direction from slope sign
if count >= 1:
if ema_val > prev_ema:
trend = +1
else if ema_val < prev_ema:
trend = -1
else:
trend = 0
strength = abs(ema_val - prev_ema) / prev_ema * 100
prev_ema = ema_val
count += 1
return (ema_val, trend, strength)
```
### Batch Processing
```csharp
var results = TtmTrend.Batch(barSeries, period: 6);
```
### Period Selection
### With Indicator Instance
```csharp
var (results, indicator) = TtmTrend.Calculate(barSeries, period: 6);
bool isBullish = indicator.Trend > 0;
double strength = indicator.Strength;
```
The default period of 6 makes TTM Trend extremely fast-reacting. The EMA half-life is approximately $\ln(2) / \ln(1 + 2/N) \approx 2.4$ bars for $N = 6$. This means the indicator responds within 2-3 bars of a price shift. Longer periods (12, 20) reduce whipsaws but delay detection. Carter's design intent was maximum responsiveness, with noise filtering delegated to companion indicators (Squeeze, Wave).
## Trading Applications
## Resources
1. **Trend Following**: Trade in the direction of the EMA color
2. **Trend Confirmation**: Use with other TTM indicators (Squeeze, Wave)
3. **Entry Timing**: Enter on color change with confirmation
4. **Exit Signal**: Exit when color changes against position
## Category
**Dynamics** - Measures trend direction and momentum using fast EMA smoothing.
## See Also
- [TTM_SQUEEZE: TTM Squeeze](../ttm_squeeze/TtmSqueeze.md)
- [TTM_WAVE: TTM Wave](../../oscillators/ttm_wave/TtmWave.md)
- [TTM_LRC: TTM Linear Regression Channel](../../channels/ttm_lrc/TtmLrc.md)
- [SUPER: SuperTrend](../super/Super.md)
- Carter, J. (2005). *Mastering the Trade*. McGraw-Hill.