Miha Kralj
6f0a339c9b
- Sar.Quantower.Tests.cs: add missing opening quote on string literal (line 48) - Exports.cs: rename Correlation.Batch → Correl.Batch (CS0103) - Ad.Validation.Tests.cs: fix Ooples OutputValues key "Ad" → "Adl"
6.5 KiB
SUPER: SuperTrend
It's not an indicator; it's a trailing stop with a marketing budget.
| Property | Value |
|---|---|
| Category | Dynamic |
| Inputs | OHLCV bar (TBar) |
| Parameters | period (default 10), multiplier (default 3.0) |
| Outputs | Multiple series (UpperBand, LowerBand) |
| Output range | Varies (see docs) |
| Warmup | > period + 1 bars |
| PineScript | super.pine |
- SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close ...
- Similar: SAR, Ghla | Complementary: ADX for trend strength | Trading note: SuperTrend; ATR-based trailing stop that flips direction. Popular in crypto and forex.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
SuperTrend is a trend-following overlay that uses ATR-scaled bands around the HL2 midpoint, switching between upper and lower bands based on close price breakouts. A ratchet mechanism prevents the active band from moving against the trend, creating a step-like trailing stop that adapts to volatility. The indicator is a two-state machine (bullish/bearish) with O(1) per-bar updates and zero allocations in the hot path.
Historical Context
Olivier Seban created SuperTrend, which gained massive popularity in the retail trading community for its visual simplicity: a single line that is green during uptrends and red during downtrends. The construction combines Wilder's ATR volatility measurement (1978) with a breakout/ratchet mechanism. Unlike moving-average crossover systems that produce continuous values, SuperTrend outputs a binary trend state with a concrete stop level, making it directly actionable as a trailing stop-loss. The indicator does not repaint historical values, though the current bar's value can oscillate until the close is finalized.
Architecture & Physics
1. Basic Bands
The raw bands center on the HL2 midpoint, offset by ATR times a multiplier:
\text{Upper}_{\text{basic}} = \frac{H_t + L_t}{2} + m \cdot \text{ATR}(N)
\text{Lower}_{\text{basic}} = \frac{H_t + L_t}{2} - m \cdot \text{ATR}(N)
where m is the multiplier (default 3.0) and N is the ATR period (default 10).
2. Ratchet Logic
The bands act as a one-way ratchet that prevents regression against the trend:
Upper band (bearish stop) can only move down:
\text{Upper}_{\text{final}} = \begin{cases} \min(\text{Upper}_{\text{basic}},\ \text{Upper}_{\text{prev}}) & \text{if } C_{t-1} \leq \text{Upper}_{\text{prev}} \\ \text{Upper}_{\text{basic}} & \text{otherwise} \end{cases}
Lower band (bullish stop) can only move up:
\text{Lower}_{\text{final}} = \begin{cases} \max(\text{Lower}_{\text{basic}},\ \text{Lower}_{\text{prev}}) & \text{if } C_{t-1} \geq \text{Lower}_{\text{prev}} \\ \text{Lower}_{\text{basic}} & \text{otherwise} \end{cases}
3. Trend State Machine
\text{Trend}_t = \begin{cases} \text{Bullish} & \text{if } C_t > \text{Upper}_{\text{final}} \\ \text{Bearish} & \text{if } C_t < \text{Lower}_{\text{final}} \\ \text{Trend}_{t-1} & \text{otherwise (hysteresis)} \end{cases}
\text{SuperTrend} = \begin{cases} \text{Lower}_{\text{final}} & \text{if Bullish} \\ \text{Upper}_{\text{final}} & \text{if Bearish} \end{cases}
The output is the active stop level. Crossing the active band flips the state.
4. Complexity
| Metric | Value |
|---|---|
| Time | O(1) per bar |
| Space | O(1) (ATR state + 2 band values + 1 trend boolean) |
| Allocations | Zero in hot path |
| Warmup | N bars (ATR stabilization) |
Mathematical Foundation
Parameters
| Parameter | Type | Default | Constraint | Description |
|---|---|---|---|---|
| atrPeriod | int | 10 | > 0 | ATR lookback period |
| multiplier | double | 3.0 | > 0 | ATR multiplier for band width |
Band Behavior by State
| State | Active Band | Ratchet Direction | Flip Condition |
|---|---|---|---|
| Bullish | Lower (support) | Can only rise | Close < Lower |
| Bearish | Upper (resistance) | Can only fall | Close > Upper |
The step-like output results from the ratchet constraint: the band remains flat until a new extremum pushes it in the trend direction. Whipsaws occur in ranging markets where close repeatedly crosses both bands.
Performance Profile
Operation Count (Streaming Mode)
Supertrend uses ATR-based bands with a state-machine ratchet: upper/lower bands only move in their respective directions, and the trend flips when price crosses the active band.
Post-warmup steady state (per bar):
| Operation | Count | Cost (cycles) | Subtotal |
|---|---|---|---|
| TR computation (SUB×3, ABS×2, MAX×2) | 7 | 1 | 7 |
| FMA (RMA ATR update) | 1 | 4 | 4 |
| MUL (ATR × multiplier) | 1 | 3 | 3 |
| ADD + SUB (upper/lower basic bands) | 2 | 1 | 2 |
| MAX/MIN (ratchet: clamp to prev band) | 2 | 1 | 2 |
| CMP × 2 (trend flip conditions) | 2 | 1 | 2 |
| CMP × 2 (final band selection) | 2 | 1 | 2 |
| Total | 19 | — | ~22 cycles |
The ratchet logic adds branch overhead (~3 cycles average from the CMPs), but overall ~22 cycles per bar.
Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
|---|---|---|
| TR + ATR (RMA) | No | Recursive RMA — sequential |
| Band arithmetic | Yes | VADDPD + VSUBPD + VMULPD after ATR pass |
| Ratchet clamp | No | State-dependent MAX/MIN — depends on prior band value |
| Trend flip state machine | No | Branch-heavy flip logic depends on prior trend state |
The ratchet and trend-flip logic create strong sequential dependencies. The ATR and band arithmetic sub-steps are vectorizable as intermediate passes.
Quality Metrics
| Metric | Score | Notes |
|---|---|---|
| Accuracy | 9/10 | FMA ATR; ratchet logic exact |
| Timeliness | 7/10 | ATR period warmup; ratchet responds immediately to band crosses |
| Smoothness | 9/10 | One-way ratchet eliminates oscillation; clean directional band |
| Noise Rejection | 8/10 | ATR-scaled bands self-adjust to volatility regime |
Resources
- Seban, O. SuperTrend indicator documentation.
- Wilder, J. W. (1978). New Concepts in Technical Trading Systems. Trend Research.