mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-16 01:28:05 +00:00
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.
114 lines
4.6 KiB
Markdown
114 lines
4.6 KiB
Markdown
# SUPER: SuperTrend
|
|
|
|
> "It's not an indicator; it's a trailing stop with a marketing budget."
|
|
|
|
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 |
|
|
|
|
### Pseudo-code
|
|
|
|
```
|
|
SUPERTREND(bar, atrPeriod=10, multiplier=3.0):
|
|
|
|
// ATR update (Wilder's smoothing or SMA)
|
|
atr = ATR.Update(bar, atrPeriod)
|
|
|
|
// Basic bands
|
|
hl2 = (bar.High + bar.Low) / 2
|
|
upper_basic = hl2 + multiplier * atr
|
|
lower_basic = hl2 - multiplier * atr
|
|
|
|
// Ratchet: upper can only decrease, lower can only increase
|
|
if prev_close <= prev_upper_final:
|
|
upper_final = min(upper_basic, prev_upper_final)
|
|
else:
|
|
upper_final = upper_basic
|
|
|
|
if prev_close >= prev_lower_final:
|
|
lower_final = max(lower_basic, prev_lower_final)
|
|
else:
|
|
lower_final = lower_basic
|
|
|
|
// State machine transition
|
|
if bar.Close > upper_final:
|
|
is_bullish = true
|
|
else if bar.Close < lower_final:
|
|
is_bullish = false
|
|
// else: retain previous state (hysteresis)
|
|
|
|
// Output active stop level
|
|
if is_bullish:
|
|
supertrend = lower_final
|
|
else:
|
|
supertrend = upper_final
|
|
|
|
return supertrend
|
|
```
|
|
|
|
### 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.
|
|
|
|
## Resources
|
|
|
|
- Seban, O. SuperTrend indicator documentation.
|
|
- Wilder, J. W. (1978). *New Concepts in Technical Trading Systems*. Trend Research.
|