QuanTAlib/lib/dynamics/adxr/Adxr.md

ADXR: Average Directional Movement Rating

ADXR smooths ADX over time, filtering out momentary strength spikes to reveal the underlying trend conviction.

Property	Value
Category	Dynamic
Inputs	OHLCV bar (TBar)
Parameters	period
Outputs	Single series (Adxr)
Output range	Varies (see docs)
Warmup	adx.WarmupPeriod + period - 1 bars
PineScript	adxr.pine

• The Average Directional Movement Rating is a smoothed version of ADX that dampens short-term fluctuations in trend strength by averaging the curren...
• Similar: ADX, DX | Complementary: Aroon for trend timing | Trading note: Smoothed ADX; slower but fewer false signals. Used in Wilder's Directional Movement System.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

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 3N bars (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.

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

Performance Profile

Operation Count (Streaming Mode)

ADXR is ADX averaged with its value N bars ago — it wraps ADX with a RingBuffer for the lag.

Post-warmup steady state (per bar):

Operation	Count	Cost (cycles)	Subtotal
ADX Update (full pipeline)	1	~79	79
RingBuffer write + oldest read	2	1	2
ADD + MUL×0.5 (average: (ADX + ADX[N]) / 2)	2	3	6
CMP (IsHot guard)	1	1	1
Total	6+ADX	—	~88 cycles

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.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
ADX calculation	Partial	See ADX analysis — recursive RMA blocks
Lag-N average	Yes	VADDPD + multiply by 0.5 once ADX array is known

The final averaging step is trivially vectorizable once the ADX time series is materialized. The bottleneck remains the ADX RMA recursion.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	Exact arithmetic; double-smoothing from underlying ADX
Timeliness	3/10	3N warmup + half-period average adds significant lag
Smoothness	9/10	Averaging two ADX instances makes it the smoothest directional indicator
Noise Rejection	9/10	Triple smoothing (2× RMA in ADX + final average) is highly noise-resistant

Resources

• Wilder, J.W. — New Concepts in Technical Trading Systems (Trend Research, 1978)
• PineScript reference: adxr.pine in indicator directory