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120 lines
5.3 KiB
Markdown
120 lines
5.3 KiB
Markdown
# TTM_TREND: TTM Trend
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> *The simplest trend indicator is the one you actually follow.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Dynamic |
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| **Inputs** | OHLCV bar (TBar) |
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| **Parameters** | `period` (default DefaultPeriod) |
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| **Outputs** | Single series (TTM_TREND) |
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| **Output range** | Varies (see docs) |
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| **Warmup** | `> 2` bars |
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| **PineScript** | [TtmTrend.pine](TtmTrend.pine) |
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- 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.
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- **Similar:** [Impulse](../impulse/Impulse.md), [AMAT](../amat/Amat.md) | **Complementary:** TTM Squeeze for timing | **Trading note:** John Carter's trend indicator; colors bars based on close vs midpoint of prior 5-bar range.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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## Historical Context
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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.
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## Architecture & Physics
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### 1. Typical Price
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$$\text{TP}_t = \frac{H_t + L_t + C_t}{3}$$
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Using typical price rather than close reduces susceptibility to closing-tick noise.
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### 2. EMA Recursion
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$$\alpha = \frac{2}{N + 1}$$
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$$\text{EMA}_t = \alpha \cdot \text{TP}_t + (1 - \alpha) \cdot \text{EMA}_{t-1}$$
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Or equivalently via FMA:
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$$\text{EMA}_t = \text{FMA}(\alpha,\ \text{TP}_t - \text{EMA}_{t-1},\ \text{EMA}_{t-1})$$
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### 3. Trend Classification
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$$\text{Trend}_t = \text{sign}(\text{EMA}_t - \text{EMA}_{t-1})$$
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| Value | State | Color |
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|:------|:------|:------|
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| +1 | Bullish | Green |
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| -1 | Bearish | Red |
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| 0 | Neutral | Gray |
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### 4. Strength Measurement
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$$\text{Strength}_t = \frac{|\text{EMA}_t - \text{EMA}_{t-1}|}{\text{EMA}_{t-1}} \times 100\%$$
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This percentage rate-of-change quantifies how aggressively the trend is moving. High strength values indicate strong conviction; near-zero values suggest potential reversal.
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### 5. Complexity
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| Metric | Value |
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|:-------|:------|
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| Time | O(1) per bar |
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| Space | O(1) (one EMA state + one previous value) |
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| Warmup | 2 bars |
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| Allocations | Zero in hot path |
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## Mathematical Foundation
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### Parameters
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| Parameter | Type | Default | Constraint | Description |
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|:----------|:-----|:--------|:-----------|:------------|
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| period | int | 6 | > 0 | EMA lookback period (very fast by default) |
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### Period Selection
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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).
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## Performance Profile
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### Operation Count (Streaming Mode)
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TTM Trend colors bars based on whether close is above/below a short SMA, with momentum confirmation from a histogram.
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**Post-warmup steady state (per bar):**
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| RingBuffer add + oldest sub (running sum) | 2 | 1 | 2 |
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| MUL × 1/N (SMA) | 1 | 3 | 3 |
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| CMP (close vs SMA) | 1 | 1 | 1 |
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| Histogram momentum (FMA EMA update) | 1 | 4 | 4 |
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| Color encoding (ternary +1/0/−1) | 1 | 1 | 1 |
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| **Total** | **6** | — | **~11 cycles** |
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Very cheap: ~11 cycles per bar at steady state.
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### Batch Mode (SIMD Analysis)
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| Operation | Vectorizable? | Notes |
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| :--- | :---: | :--- |
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| SMA (rolling sum) | Yes | VADDPD + prefix-sum subtract-lag |
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| EMA histogram | **No** | Recursive IIR |
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| Bar color comparison | Yes | VCMPPD |
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The EMA histogram is the only sequential step. SMA and comparison are fully vectorizable.
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 10/10 | SMA exact arithmetic; EMA FMA-precise |
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| **Timeliness** | 8/10 | Short SMA period dominates; near-instantaneous response |
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| **Smoothness** | 10/10 | Ternary output — maximally smooth |
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| **Noise Rejection** | 6/10 | Short SMA period makes it sensitive to noise in choppy markets |
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## Resources
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- Carter, J. (2005). *Mastering the Trade*. McGraw-Hill. |