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.
4.6 KiB
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.