Miha Kralj
90d5638008
- 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.
3.5 KiB
TTM_TREND: TTM Trend
"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 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.
Architecture & Physics
1. Typical Price
\text{TP}_t = \frac{H_t + L_t + C_t}{3}
Using typical price rather than close reduces susceptibility to closing-tick noise.
2. EMA Recursion
\alpha = \frac{2}{N + 1}
\text{EMA}_t = \alpha \cdot \text{TP}_t + (1 - \alpha) \cdot \text{EMA}_{t-1}
Or equivalently via FMA:
\text{EMA}_t = \text{FMA}(\alpha,\ \text{TP}_t - \text{EMA}_{t-1},\ \text{EMA}_{t-1})
3. Trend Classification
\text{Trend}_t = \text{sign}(\text{EMA}_t - \text{EMA}_{t-1})
| 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 | O(1) per bar |
| Space | O(1) (one EMA state + one previous value) |
| Warmup | 2 bars |
| Allocations | Zero in hot path |
Mathematical Foundation
Parameters
| Parameter | Type | Default | Constraint | Description |
|---|---|---|---|---|
| period | int | 6 | > 0 | EMA lookback period (very fast by default) |
Pseudo-code
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)
Period Selection
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).
Resources
- Carter, J. (2005). Mastering the Trade. McGraw-Hill.