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147 lines
6.1 KiB
Markdown
147 lines
6.1 KiB
Markdown
# ADXR: Average Directional Movement Rating
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Dynamic |
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| **Inputs** | OHLCV bar (TBar) |
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| **Parameters** | `period` |
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| **Outputs** | Single series (Adxr) |
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| **Output range** | Varies (see docs) |
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| **Warmup** | `adx.WarmupPeriod + period - 1` bars |
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### TL;DR
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- The Average Directional Movement Rating is a smoothed version of ADX that dampens short-term fluctuations in trend strength by averaging the curren...
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- Parameterized by `period`.
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- Output range: Varies (see docs).
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- Requires `adx.WarmupPeriod + period - 1` bars of warmup before first valid output (IsHot = true).
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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## Historical Context
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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.
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## Architecture & Physics
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### 1. ADX Dependency
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ADXR is a composite indicator that does not interact with price directly. It instantiates and maintains a full ADX pipeline internally:
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$$\text{Price} \rightarrow \text{DM/TR} \rightarrow \text{RMA} \rightarrow \text{DI} \rightarrow \text{DX} \rightarrow \text{ADX} \rightarrow \text{ADXR}$$
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### 2. Historical Buffer
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A circular buffer of size $N$ stores historical ADX values, providing $O(1)$ access to the value from $N-1$ bars ago.
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### 3. Rating Calculation
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$$ADXR_t = \frac{ADX_t + ADX_{t-(N-1)}}{2}$$
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The $N-1$ lag (rather than $N$) matches TA-Lib's reference implementation exactly.
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### 4. Complexity
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- **Time:** $O(1)$ per bar — ADX update plus one buffer lookup and one average
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- **Space:** $O(N)$ — circular buffer for ADX history
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- **Warmup:** $\approx 3N$ bars (ADX convergence + buffer fill)
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## Mathematical Foundation
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### Parameters
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| Symbol | Parameter | Default | Constraint |
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|--------|-----------|---------|------------|
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| $N$ | period | 14 | $N \geq 2$ |
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The period controls both the internal ADX calculation and the historical lookback depth.
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### Pseudo-code
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```
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Initialize:
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adx = new Adx(period)
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adxBuffer = RingBuffer(period)
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bar_count = 0
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On each bar (high, low, close, isNew):
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if !isNew: restore previous state
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// Full ADX pipeline
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adxValue = adx.Update(high, low, close, isNew)
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// Store in history
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adxBuffer.Add(adxValue)
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bar_count++
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// ADXR = average of current and (N-1)-lagged ADX
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if bar_count >= period:
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historicalAdx = adxBuffer[0] // oldest value in buffer
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ADXR = (adxValue + historicalAdx) / 2.0
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else:
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ADXR = adxValue // insufficient history
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output = ADXR
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```
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### Lag Analysis
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| Component | Lag Source |
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|-----------|-----------|
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| DM → RMA | $\approx N$ bars (Wilder smoothing) |
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| DX → ADX | $\approx N$ bars (second RMA) |
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| ADX → ADXR | $N-1$ bars (historical average) |
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| **Total effective lag** | $\approx 3N - 1$ bars |
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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.
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### Regime Classification
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| ADXR Value | Interpretation |
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|------------|----------------|
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| < 20 | Sustained range-bound; favor mean-reversion |
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| 20–25 | Ambiguous regime; reduce position sizing |
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| > 25 | Sustained trending; favor momentum strategies |
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## Performance Profile
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### Operation Count (Streaming Mode)
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ADXR is ADX averaged with its value N bars ago — it wraps ADX with a RingBuffer for the lag.
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**Post-warmup steady state (per bar):**
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| ADX Update (full pipeline) | 1 | ~79 | 79 |
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| RingBuffer write + oldest read | 2 | 1 | 2 |
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| ADD + MUL×0.5 (average: (ADX + ADX[N]) / 2) | 2 | 3 | 6 |
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| CMP (IsHot guard) | 1 | 1 | 1 |
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| **Total** | **6+ADX** | — | **~88 cycles** |
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ADXR requires 3N bars of warmup: N for ADX initialization, N for ADX smoothing, N for the lookback buffer. For default $N=14$: ~88 cycles per bar.
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### Batch Mode (SIMD Analysis)
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| Operation | Vectorizable? | Notes |
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| :--- | :---: | :--- |
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| ADX calculation | Partial | See ADX analysis — recursive RMA blocks |
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| Lag-N average | Yes | VADDPD + multiply by 0.5 once ADX array is known |
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The final averaging step is trivially vectorizable once the ADX time series is materialized. The bottleneck remains the ADX RMA recursion.
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 9/10 | Exact arithmetic; double-smoothing from underlying ADX |
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| **Timeliness** | 3/10 | 3N warmup + half-period average adds significant lag |
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| **Smoothness** | 9/10 | Averaging two ADX instances makes it the smoothest directional indicator |
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| **Noise Rejection** | 9/10 | Triple smoothing (2× RMA in ADX + final average) is highly noise-resistant |
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## Resources
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- Wilder, J.W. — *New Concepts in Technical Trading Systems* (Trend Research, 1978)
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- PineScript reference: `adxr.pine` in indicator directory
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