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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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> "The average candlestick body reveals the market's true conviction."
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Developed by Tushar Chande, the Qstick indicator measures the average difference between closing and opening prices over a lookback period. It quantifies whether bars are predominantly bullish (closing above opens) or bearish (closing below opens), providing a smoothed view of candlestick body direction and magnitude.
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The Qstick indicator, developed by Tushar Chande, computes a moving average of the close-minus-open difference over a lookback period, quantifying whether bars are predominantly bullish or bearish. Positive values indicate closes above opens (buying pressure); negative values indicate closes below opens (selling pressure). It supports both SMA (O(N) space via ring buffer) and EMA (O(1) space) smoothing modes and requires TBar input for open/close access.
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## Historical Context
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Tushar Chande introduced the Qstick as part of his work on candlestick pattern quantification in the early 1990s. While traditional candlestick analysis relies on visual pattern recognition, Qstick provides a numerical measure that can be systematically tracked and used for algorithmic trading.
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Tushar Chande introduced Qstick as part of his candlestick quantification work in *The New Technical Trader* (1994, co-authored with Stanley Kroll). Traditional candlestick analysis relies on visual pattern recognition; Qstick reduces bar body direction and magnitude to a single continuous number suitable for systematic tracking. The indicator addresses a specific gap: close-to-close momentum indicators miss intrabar dynamics captured by the open-to-close differential. The name "Qstick" reflects the "quick stick" reading of candlestick conviction.
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The indicator addresses a fundamental question: "On average, are prices closing higher or lower than they open?" This simple metric captures intrabar momentum that other indicators measuring close-to-close changes may miss.
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## Architecture & Physics
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## Architecture
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### 1. Body Difference
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### 1. Body Difference Calculation
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$$d_t = \text{Close}_t - \text{Open}_t$$
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The core input is the difference between close and open:
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```
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diff = Close - Open
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```
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- **Positive diff**: Bullish bar (white/green candle)
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- **Negative diff**: Bearish bar (black/red candle)
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- **Zero diff**: Doji (open equals close)
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Positive $d_t$ represents a bullish bar (close above open), negative represents bearish, zero represents a doji.
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### 2. Moving Average Smoothing
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The raw differences are smoothed using either SMA or EMA:
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**SMA mode:** Maintains a ring buffer of $N$ differences and a running sum for O(1) incremental updates:
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**SMA Mode:**
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$$\text{Qstick} = \frac{1}{n} \sum_{i=0}^{n-1} (Close_i - Open_i)$$
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$$\text{Qstick}_t = \frac{1}{N} \sum_{i=0}^{N-1} d_{t-i}$$
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**EMA Mode:**
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$$\text{Qstick}_t = \alpha \cdot diff_t + (1 - \alpha) \cdot \text{Qstick}_{t-1}$$
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**EMA mode:** Standard recursive filter with decay $\alpha = 2/(N+1)$:
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where $\alpha = \frac{2}{period + 1}$
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$$\text{Qstick}_t = \alpha \cdot d_t + (1 - \alpha) \cdot \text{Qstick}_{t-1}$$
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### 3. State Management
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EMA mode uses O(1) space but weights recent bars more heavily than SMA.
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For real-time bar correction (isNew=false), the indicator maintains:
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- `_sum` / `_savedSum`: Running sum for SMA
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- `_emaValue` / `_savedEmaValue`: Current EMA value
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- `_count` / `_savedCount`: Bar count for warmup
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### 3. Complexity
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## Parameters
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| Parameter | Type | Default | Valid Range | Description |
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|-----------|------|---------|-------------|-------------|
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| `period` | int | 14 | ≥ 1 | Lookback period for moving average |
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| `useEma` | bool | false | true/false | Use EMA (true) or SMA (false) |
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| Metric | SMA Mode | EMA Mode |
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|:-------|:---------|:---------|
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| Time | O(1) per bar | O(1) per bar |
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| Space | O(N) ring buffer | O(1) |
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| Ops | 1 add, 1 sub, 1 div | 1 sub, 1 mul, 1 FMA |
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## Mathematical Foundation
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### Formula
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### Parameters
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| Parameter | Type | Default | Constraint | Description |
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|:----------|:-----|:--------|:-----------|:------------|
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| period | int | 14 | > 0 | Lookback period for moving average |
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| useEma | bool | false | — | Use EMA (true) or SMA (false) |
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### Pseudo-code
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```
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Qstick = MA(Close - Open, period)
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QSTICK(bar, period=14, useEma=false):
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diff = bar.Close - bar.Open
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if useEma:
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// EMA mode
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alpha = 2.0 / (period + 1)
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if count == 0:
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ema_val = diff
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else:
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ema_val = FMA(alpha, diff - ema_val, ema_val) // alpha*(diff-ema)+ema
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result = ema_val
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else:
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// SMA mode with ring buffer
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if buffer is full:
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running_sum -= buffer.oldest
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buffer.add(diff)
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running_sum += diff
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result = running_sum / min(count, period)
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return result
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```
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### Interpretation
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### Zero-Crossing Interpretation
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| Qstick Value | Market Condition |
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|--------------|------------------|
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| > 0 | Bullish momentum (closes above opens) |
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| < 0 | Bearish momentum (closes below opens) |
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| = 0 | Neutral (balanced open/close) |
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| Rising | Increasing bullish pressure |
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| Falling | Increasing bearish pressure |
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| Condition | Meaning |
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|:----------|:--------|
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| Qstick > 0 | Closes above opens dominate (net buying pressure) |
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| Qstick < 0 | Closes below opens dominate (net selling pressure) |
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| Qstick crosses zero | Shift in intrabar momentum direction |
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| Qstick rising | Increasing bullish pressure regardless of sign |
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| Qstick falling | Increasing bearish pressure regardless of sign |
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### Signal Generation
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### Scale Dependence
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- **Buy Signal**: Qstick crosses above zero
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- **Sell Signal**: Qstick crosses below zero
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- **Divergence**: Price making new highs while Qstick making lower highs suggests weakening momentum
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Qstick values are in absolute price units, not normalized. Cross-instrument comparison requires normalization (e.g., divide by ATR or price level). Short periods (5-8) suit trading signals; longer periods (20+) suit trend identification.
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## Performance Profile
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## Resources
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### Operation Count (Streaming Mode)
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| Operation | SMA Mode | EMA Mode |
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|-----------|----------|----------|
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| ADD/SUB | 3 | 2 |
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| MUL | 0 | 1 |
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| DIV | 1 | 0 |
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| FMA | 0 | 1 |
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| Memory | O(period) | O(1) |
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### Complexity
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- **Time**: O(1) per bar for both modes
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- **Space**: O(period) for SMA, O(1) for EMA
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### Quality Metrics
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| Metric | Score | Notes |
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|--------|-------|-------|
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| Accuracy | 10/10 | Exact calculation |
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| Timeliness | 8/10 | Lag proportional to period |
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| Overshoot | 2/10 | Smooth, no overshoot |
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| Smoothness | 8/10 | SMA smoother than EMA |
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## Validation
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| Library | Status | Notes |
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|---------|--------|-------|
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| TA-Lib | ✓ | Not available (implement locally) |
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| Skender | ✓ | Validated against Qstick |
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| OoplesFinance | ✓ | Validated |
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## Common Pitfalls
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1. **Ignoring Volume**: Qstick weights all bars equally; consider volume-weighted variants for more accuracy
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2. **Range Dependence**: Absolute values depend on price scale; normalize for comparison across instruments
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3. **Period Selection**: Short periods (5-8) for trading signals; long periods (20+) for trend identification
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4. **Gap Sensitivity**: Large gaps (open ≠ previous close) can distort readings
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5. **Flat Markets**: Near-zero readings indicate indecision, not necessarily reversal
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## Usage Example
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```csharp
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// Create Qstick with 14-period SMA
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var qstick = new Qstick(14);
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// Update with bar data
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foreach (var bar in bars)
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{
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var result = qstick.Update(bar);
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if (qstick.IsHot)
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{
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Console.WriteLine($"Qstick: {result.Value:F4}");
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}
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}
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// Or use EMA mode
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var qstickEma = new Qstick(14, useEma: true);
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```
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## References
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1. Chande, T. S. (1994). *The New Technical Trader*. John Wiley & Sons.
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2. Chande, T. S., & Kroll, S. (1994). *Beyond Technical Analysis*. John Wiley & Sons.
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3. Kirkpatrick, C. D., & Dahlquist, J. R. (2015). *Technical Analysis: The Complete Resource for Financial Market Technicians*. FT Press.
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- Chande, T. S. & Kroll, S. (1994). *The New Technical Trader*. John Wiley and Sons.
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- Kirkpatrick, C. D. & Dahlquist, J. R. (2015). *Technical Analysis: The Complete Resource for Financial Market Technicians*. FT Press.
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