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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.
79 lines
4.3 KiB
Markdown
79 lines
4.3 KiB
Markdown
# RWMA: Range Weighted Moving Average
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> "Most averages weight by position: recent bars matter more. RWMA weights by volatility: volatile bars matter more. The market spoke loudest when the range was widest, so listen to those bars."
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RWMA weights each bar's contribution to the average by its price range (high minus low), giving greater influence to volatile bars and less to narrow-range, indecisive bars. The logic: a bar with a large range represents stronger price discovery and carries more informational content than a low-range doji. This produces a moving average that gravitates toward prices established during high-activity periods, naturally incorporating volatility as a relevance signal without requiring a separate volatility indicator.
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## Historical Context
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Range-weighted averaging is a practical adaptation of the general concept of precision-weighted means from statistics, where observations are weighted by the inverse of their variance (or, equivalently, by their "importance" or precision). In financial applications, bar range serves as a real-time proxy for intra-bar volatility, available without the computational overhead of standard deviation or ATR calculations.
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The concept appears informally in trading literature from the 1990s, often attributed to floor-trader heuristics: "wide-range bars lead price," meaning that the closing prices of high-range bars tend to be more predictive of subsequent direction than those of narrow-range bars. RWMA formalizes this heuristic into a weighted average.
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Unlike position-weighted averages (WMA, EMA) where the weighting scheme is fixed by the period, RWMA's weights are data-adaptive. The weight vector changes every bar based on the range profile of the lookback window. This makes RWMA inherently non-stationary: two windows with identical closing prices but different range profiles produce different RWMA values. The data-adaptive property also means RWMA cannot be expressed as a fixed-coefficient FIR filter, though its computation is structurally similar.
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RWMA requires high and low price data (TBar inputs), making it inapplicable to single-valued series. When all bars have zero range (constant price), the denominator collapses to zero and the filter falls back to the raw source price.
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## Architecture & Physics
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### 1. Weight Computation
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For each bar $i$ in the lookback window:
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$$
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w_i = \max(\text{High}_i - \text{Low}_i, 0)
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$$
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The $\max$ clamp ensures non-negative weights (relevant for synthetic data where high $<$ low might occur due to data errors).
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### 2. Weighted Average
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$$
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\text{RWMA} = \frac{\sum_{i=0}^{N-1} \text{Close}_i \cdot w_i}{\sum_{i=0}^{N-1} w_i}
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$$
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If $\sum w_i = 0$ (all bars have zero range), the output degenerates to the current source price.
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### 3. TBar Requirement
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RWMA consumes TBar data (OHLC), not single-valued TValue. The C# implementation should accept `TBar` inputs and route `High`, `Low`, `Close` appropriately.
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## Mathematical Foundation
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Given a window of $N$ bars with close prices $c_i$, highs $h_i$, and lows $l_i$ (where $i = 0$ is newest):
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$$
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\text{RWMA}_t = \frac{\sum_{i=0}^{N-1} c_{t-i} \cdot (h_{t-i} - l_{t-i})}{\sum_{i=0}^{N-1} (h_{t-i} - l_{t-i})}
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$$
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**Properties:**
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- **Convex combination:** All weights are non-negative, so the output is bounded by $[\min(c_i), \max(c_i)]$ within the window. No overshoot possible.
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- **Adaptive lag:** Lag shifts toward the position of the highest-range bars. If the most volatile bar is recent, lag decreases; if it is old, lag increases.
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- **Degeneracy:** When all ranges are zero, $\text{RWMA} = c_t$ (current close).
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**Complexity:** O(N) per bar (single pass over the window).
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**Default parameters:** `period = 14`, `minPeriod = 1`.
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**Pseudo-code (streaming):**
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```
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sumWV = 0; sumW = 0
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for i = 0 to period-1:
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range = max(high[i] - low[i], 0)
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sumWV += close[i] * range
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sumW += range
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if sumW > 0:
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return sumWV / sumW
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else:
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return close[0]
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```
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## Resources
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- Bollinger, J. (2001). *Bollinger on Bollinger Bands*. McGraw-Hill. (Discusses range-based volatility measures in the context of band-width indicators.)
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- Achelis, S.B. (2000). *Technical Analysis from A to Z*, 2nd ed. McGraw-Hill.
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- Garman, M.B. & Klass, M.J. (1980). "On the Estimation of Security Price Volatilities from Historical Data." *Journal of Business*, 53(1), 67-78. (Range-based volatility estimation from OHLC data.)
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