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.
3.8 KiB
ADXR: Average Directional Movement Rating
The Average Directional Movement Rating is a smoothed version of ADX that dampens short-term fluctuations in trend strength by averaging the current ADX with a historical ADX value. This creates a doubly-lagged metric that sacrifices all timing utility in exchange for stable regime classification. ADXR answers one question: does the current market environment reward trend-following strategies? If ADXR is high, deploy momentum logic. If low, deploy mean-reversion. It is a strategic filter, not a tactical signal.
Historical Context
J. Welles Wilder Jr. introduced ADXR alongside ADX in New Concepts in Technical Trading Systems (1978). His reasoning was pragmatic: ADX itself can be erratic during transitions between trending and ranging regimes, producing whipsaw readings that confuse systematic allocation. By averaging the current ADX with its value from N-1 bars ago, Wilder created a "momentum of momentum" indicator smoothed to geological stability. The ADXR found its architectural niche not as a trading signal but as a capital allocation filter — determining whether a trend-following system should be active at all. Its double lag (ADX already lags price; ADXR lags ADX) makes it useless for entry timing by design.
Architecture & Physics
1. ADX Dependency
ADXR is a composite indicator that does not interact with price directly. It instantiates and maintains a full ADX pipeline internally:
\text{Price} \rightarrow \text{DM/TR} \rightarrow \text{RMA} \rightarrow \text{DI} \rightarrow \text{DX} \rightarrow \text{ADX} \rightarrow \text{ADXR}
2. Historical Buffer
A circular buffer of size N stores historical ADX values, providing O(1) access to the value from N-1 bars ago.
3. Rating Calculation
ADXR_t = \frac{ADX_t + ADX_{t-(N-1)}}{2}
The N-1 lag (rather than N) matches TA-Lib's reference implementation exactly.
4. Complexity
- Time:
O(1)per bar — ADX update plus one buffer lookup and one average - Space:
O(N)— circular buffer for ADX history - Warmup:
\approx 3Nbars (ADX convergence + buffer fill)
Mathematical Foundation
Parameters
| Symbol | Parameter | Default | Constraint |
|---|---|---|---|
N |
period | 14 | N \geq 2 |
The period controls both the internal ADX calculation and the historical lookback depth.
Pseudo-code
Initialize:
adx = new Adx(period)
adxBuffer = RingBuffer(period)
bar_count = 0
On each bar (high, low, close, isNew):
if !isNew: restore previous state
// Full ADX pipeline
adxValue = adx.Update(high, low, close, isNew)
// Store in history
adxBuffer.Add(adxValue)
bar_count++
// ADXR = average of current and (N-1)-lagged ADX
if bar_count >= period:
historicalAdx = adxBuffer[0] // oldest value in buffer
ADXR = (adxValue + historicalAdx) / 2.0
else:
ADXR = adxValue // insufficient history
output = ADXR
Lag Analysis
| Component | Lag Source |
|---|---|
| DM → RMA | \approx N bars (Wilder smoothing) |
| DX → ADX | \approx N bars (second RMA) |
| ADX → ADXR | N-1 bars (historical average) |
| Total effective lag | \approx 3N - 1 bars |
For the default period of 14, ADXR carries roughly 41 bars of effective lag. This is a feature, not a limitation — it ensures that only sustained regime changes register in the output.
Regime Classification
| ADXR Value | Interpretation |
|---|---|
| < 20 | Sustained range-bound; favor mean-reversion |
| 20–25 | Ambiguous regime; reduce position sizing |
| > 25 | Sustained trending; favor momentum strategies |
Resources
- Wilder, J.W. — New Concepts in Technical Trading Systems (Trend Research, 1978)
- PineScript reference:
adxr.pinein indicator directory