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Add new moving average implementations: LTMA, MCNMA, NLMA, NMA, NYQMA, RAIN, and TRAMA
- 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.
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Miha Kralj
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# TTM_SQUEEZE: TTM Squeeze
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> **Pending Implementation** - Placeholder for John Carter's TTM Squeeze indicator
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> "Volatility compression is the market holding its breath before screaming."
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John Carter's TTM Squeeze detects low-volatility compression by comparing Bollinger Band width against Keltner Channel width: when BB fits inside KC, a "squeeze" is on, signaling imminent breakout. The momentum component uses linear regression of price deviation from the Donchian midline to indicate direction. The indicator outputs a boolean squeeze state plus a continuous momentum histogram, requiring BB(20,2.0) and KC(20,1.5) as default parameters with a combined warmup of 20 bars.
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## Historical Context
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John Carter developed TTM Squeeze as his signature volatility breakout indicator, popularized through his book *Mastering the Trade* and thinkorswim platform. The indicator combines Bollinger Bands and Keltner Channels to identify low-volatility "squeeze" conditions that typically precede explosive price moves.
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John Carter developed TTM Squeeze as his signature volatility breakout indicator, popularized through *Mastering the Trade* (2005) and the thinkorswim platform. The core insight combines two independent volatility measures: Bollinger's standard-deviation bands and Keltner's ATR-based channels. When the faster-reacting BB contracts inside the slower KC, it signals unusually low volatility, a condition that reliably precedes explosive directional moves. Carter added a momentum oscillator based on linear regression to provide directional bias during squeeze releases. The indicator became one of the most widely used proprietary tools in retail trading.
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## Algorithm
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## Architecture & Physics
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### Squeeze Detection
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- **Squeeze On (●):** Bollinger Bands inside Keltner Channel
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- **Squeeze Off (○):** Bollinger Bands outside Keltner Channel
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### 1. Bollinger Band Width
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$$\text{BB}_{\text{upper}} = \text{SMA}(C, N_{\text{BB}}) + k_{\text{BB}} \cdot \sigma(C, N_{\text{BB}})$$
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$$\text{BB}_{\text{lower}} = \text{SMA}(C, N_{\text{BB}}) - k_{\text{BB}} \cdot \sigma(C, N_{\text{BB}})$$
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where $N_{\text{BB}} = 20$, $k_{\text{BB}} = 2.0$, and $\sigma$ is population standard deviation.
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### 2. Keltner Channel Width
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$$\text{KC}_{\text{upper}} = \text{EMA}(C, N_{\text{KC}}) + k_{\text{KC}} \cdot \text{ATR}(N_{\text{KC}})$$
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$$\text{KC}_{\text{lower}} = \text{EMA}(C, N_{\text{KC}}) - k_{\text{KC}} \cdot \text{ATR}(N_{\text{KC}})$$
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where $N_{\text{KC}} = 20$, $k_{\text{KC}} = 1.5$.
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### 3. Squeeze Detection
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$$\text{SqueezeOn} = (\text{BB}_{\text{lower}} > \text{KC}_{\text{lower}}) \text{ and } (\text{BB}_{\text{upper}} < \text{KC}_{\text{upper}})$$
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When BB fits entirely inside KC, the squeeze is active. The first bar where squeeze transitions from on to off ("squeeze fires") signals the breakout.
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### 4. Momentum Histogram
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$$\text{midline} = \frac{\text{Highest}(H, N) + \text{Lowest}(L, N)}{2}$$
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$$\delta_t = C_t - \frac{\text{midline}_t + \text{SMA}(C, N)}{2}$$
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$$\text{Momentum} = \text{LinReg}(\delta, N)$$
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The linear regression extracts the trend component of the deviation, filtering noise. Momentum sign indicates direction; slope indicates acceleration.
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### 5. Momentum Color States
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| Color | Condition |
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|:------|:----------|
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| Cyan | Momentum > 0 and rising |
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| Blue | Momentum > 0 and falling |
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| Red | Momentum < 0 and falling |
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| Yellow | Momentum < 0 and rising |
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### 6. Complexity
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| Metric | Value |
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|:-------|:------|
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| Time | O(1) per bar (incremental BB, KC, LinReg updates) |
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| Space | O(N) for sliding window buffers (SMA, StdDev, ATR, high/low, LinReg) |
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| Warmup | N bars (default 20) |
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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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| bbLength | int | 20 | > 1 | Bollinger Band period |
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| bbMult | double | 2.0 | > 0 | BB standard deviation multiplier |
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| kcLength | int | 20 | > 1 | Keltner Channel period |
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| kcMult | double | 1.5 | > 0 | KC ATR multiplier |
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### Pseudo-code
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### Momentum Histogram
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Linear regression of price deviation from 20-period midline:
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```
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midline = (Highest(20) + Lowest(20)) / 2
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momentum = LinReg(close - midline, 20)
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TTM_SQUEEZE(bar, bbLen=20, bbMult=2.0, kcLen=20, kcMult=1.5):
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// Bollinger Bands
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sma_val = SMA(close, bbLen)
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stddev = StdDev(close, bbLen)
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bb_upper = sma_val + bbMult * stddev
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bb_lower = sma_val - bbMult * stddev
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// Keltner Channel
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ema_val = EMA(close, kcLen)
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atr_val = ATR(bar, kcLen)
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kc_upper = ema_val + kcMult * atr_val
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kc_lower = ema_val - kcMult * atr_val
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// Squeeze state
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squeeze_on = (bb_lower > kc_lower) AND (bb_upper < kc_upper)
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// Momentum via linear regression of deviation
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highest_high = Highest(high, bbLen)
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lowest_low = Lowest(low, bbLen)
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midline = (highest_high + lowest_low) / 2
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delta = close - (midline + sma_val) / 2
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momentum = LinReg(delta, bbLen)
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// Momentum direction
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momentum_rising = momentum > prev_momentum
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momentum_positive = momentum > 0
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return (momentum, squeeze_on, momentum_rising, momentum_positive)
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```
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### Color Coding
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- **Cyan:** Momentum rising above zero
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- **Blue:** Momentum falling but above zero
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- **Red:** Momentum falling below zero
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- **Yellow:** Momentum rising but below zero
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### Squeeze-Fire Signal
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## Default Parameters
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The critical trading signal occurs on the transition bar:
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| Parameter | Value | Description |
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|:----------|:------|:------------|
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| BB Length | 20 | Bollinger Band period |
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| BB Mult | 2.0 | Bollinger Band standard deviation multiplier |
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| KC Length | 20 | Keltner Channel period |
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| KC Mult | 1.5 | Keltner Channel ATR multiplier |
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$$\text{SqueezeFired}_t = \text{SqueezeOn}_{t-1} \text{ and } \neg\text{SqueezeOn}_t$$
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## Outputs
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Combined with momentum direction, this yields entry signals: long when squeeze fires with positive rising momentum, short when squeeze fires with negative falling momentum.
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| Output | Type | Description |
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|:-------|:-----|:------------|
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| Momentum | double | Linear regression momentum value |
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| SqueezeOn | bool | True when BB inside KC |
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| MomentumRising | bool | True when momentum increasing |
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| MomentumPositive | bool | True when momentum > 0 |
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## Resources
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## Trading Signals
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1. **Squeeze Fired:** First bar where SqueezeOn transitions to false
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2. **Long Entry:** Squeeze fires + momentum positive + momentum rising
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3. **Short Entry:** Squeeze fires + momentum negative + momentum falling
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## Category
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**Dynamics** - Measures volatility compression and subsequent momentum release.
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## See Also
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- [BBS: Bollinger Band Squeeze](../../oscillators/bbs/Bbs.md)
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- [BBW: Bollinger Band Width](../../volatility/bbw/Bbw.md)
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- [KCHANNEL: Keltner Channel](../../channels/kchannel/Kchannel.md)
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- [TTM: TTM Trend](../ttm/Ttm.md)
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- Carter, J. (2005). *Mastering the Trade*. McGraw-Hill.
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- Bollinger, J. (2001). *Bollinger on Bollinger Bands*. McGraw-Hill.
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- Keltner, C. (1960). *How to Make Money in Commodities*. The Keltner Statistical Service.
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