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.
4.3 KiB
RWMA: Range Weighted Moving Average
"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."
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.
Historical Context
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.
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.
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.
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.
Architecture & Physics
1. Weight Computation
For each bar i in the lookback window:
w_i = \max(\text{High}_i - \text{Low}_i, 0)
The \max clamp ensures non-negative weights (relevant for synthetic data where high < low might occur due to data errors).
2. Weighted Average
\text{RWMA} = \frac{\sum_{i=0}^{N-1} \text{Close}_i \cdot w_i}{\sum_{i=0}^{N-1} w_i}
If \sum w_i = 0 (all bars have zero range), the output degenerates to the current source price.
3. TBar Requirement
RWMA consumes TBar data (OHLC), not single-valued TValue. The C# implementation should accept TBar inputs and route High, Low, Close appropriately.
Mathematical Foundation
Given a window of N bars with close prices c_i, highs h_i, and lows l_i (where i = 0 is newest):
\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})}
Properties:
- 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. - 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.
- Degeneracy: When all ranges are zero,
\text{RWMA} = c_t(current close).
Complexity: O(N) per bar (single pass over the window).
Default parameters: period = 14, minPeriod = 1.
Pseudo-code (streaming):
sumWV = 0; sumW = 0
for i = 0 to period-1:
range = max(high[i] - low[i], 0)
sumWV += close[i] * range
sumW += range
if sumW > 0:
return sumWV / sumW
else:
return close[0]
Resources
- Bollinger, J. (2001). Bollinger on Bollinger Bands. McGraw-Hill. (Discusses range-based volatility measures in the context of band-width indicators.)
- Achelis, S.B. (2000). Technical Analysis from A to Z, 2nd ed. McGraw-Hill.
- 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.)