QuanTAlib/lib/volatility/atrn/Atrn.md

ATRN: Average True Range Normalized

Context is everything. A $5 ATR means nothing until you know the $5 ATR from last month was $2.

Property	Value
Category	Volatility
Inputs	OHLCV bar (TBar)
Parameters	period
Outputs	Single series (Atrn)
Output range	\geq 0
Warmup	1 bar
PineScript	atrn.pine

• ATRN transforms the absolute ATR into a relative measure by normalizing it to a [0,1] scale using min-max scaling over a lookback window.
• Similar: ATR, NATR | Complementary: Position sizing | Trading note: Normalized ATR; percentage-based for cross-asset comparison.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

ATRN transforms the absolute ATR into a relative measure by normalizing it to a [0,1] scale using min-max scaling over a lookback window. This answers the question: "Is current volatility high or low compared to recent history?"

While ATR tells you how much an asset moves, ATRN tells you how unusual that movement is relative to the asset's own recent behavior. A value near 1 means volatility is at its recent high; a value near 0 means volatility is at its recent low; 0.5 means volatility is average.

Historical Context

ATRN is a practical extension of Wilder's ATR, developed to solve the context problem in volatility analysis. Raw ATR values are meaningless in isolation—you need to compare them to something. Some traders compare ATR to price (NATR), which gives a percentage. ATRN takes a different approach: it compares ATR to its own recent range.

This normalization approach is common in machine learning and signal processing, where inputs are scaled to [0,1] for better model performance. ATRN applies the same principle to volatility measurement.

Architecture & Physics

ATRN is built on three components:

1. True Range (TR): Captures the full range of price movement including gaps.
2. RMA Smoothing: Wilder's exponential average (\alpha = 1/N) to smooth TR into ATR.
3. Min-Max Normalization: Scales ATR to [0,1] over a lookback window.

The Lookback Window

The lookback window is set to 10 \times period. For the default period of 14:

• Lookback = 140 bars
• This captures roughly 6-7 months of daily data
• Provides stable min/max anchors while remaining responsive to regime changes

Edge Case: Constant Volatility

When max ATR equals min ATR (perfectly constant volatility), the denominator becomes zero. ATRN returns 0.5 in this case—the midpoint—indicating "average" volatility by default.

Mathematical Foundation

1. True Range (TR)

TR_t = \max(H_t - L_t, |H_t - C_{t-1}|, |L_t - C_{t-1}|)

2. Average True Range (ATR)

ATR_t = \frac{ATR_{t-1} \times (N-1) + TR_t}{N}

3. Min-Max Normalization

ATRN_t = \frac{ATR_t - \min(ATR, W)}{\max(ATR, W) - \min(ATR, W)}

Where:

• W = 10 \times N (lookback window)
• \min(ATR, W) = minimum ATR over last W bars
• \max(ATR, W) = maximum ATR over last W bars

If \max = \min:

ATRN_t = 0.5

Performance Profile

Operation Count (Streaming Mode)

ATRN normalizes ATR to [0,1] using min/max over a lookback window — O(1) chained computation.

Operation	Count	Cost (cycles)	Subtotal
ATR (Wilder EMA of TR)	1	8 cy	~8 cy
RingBuffer min-ATR update (lookback)	1	4 cy	~4 cy
RingBuffer max-ATR update (lookback)	1	4 cy	~4 cy
ATRN = (ATR - min) / (max - min)	1	5 cy	~5 cy
Zero-range guard	1	2 cy	~2 cy
NaN guard + state update	1	2 cy	~2 cy
Total	O(1)	—	~25 cy

O(1) chained ATR + normalization. Two separate warmup phases: ATR needs period bars, then ATRN needs lookback bars for valid min/max range.

Metric	Score	Notes
Throughput	9	High; O(W) for min-max scan per bar.
Allocations	0	Zero-allocation in hot paths via RingBuffer.
Complexity	O(W)	Linear in lookback window size.
Accuracy	10	Exact min-max normalization.
Timeliness	5	Lags due to RMA + lookback window context.
Overshoot	0	Bounded to [0,1] by construction.
Smoothness	8	Inherits RMA smoothness from ATR.

Validation

Library	Status	Notes
QuanTAlib	✅	Reference implementation.
TA-Lib	N/A	No direct equivalent; underlying ATR validated.
Skender	N/A	No direct equivalent; underlying ATR validated.
Tulip	N/A	No direct equivalent.
Ooples	N/A	No direct equivalent.

ATRN is a QuanTAlib-specific indicator. Validation confirms:

1. Underlying ATR matches external libraries.
2. Normalization formula produces values in [0,1].
3. Constant volatility produces 0.5.
4. Increasing volatility approaches 1.0.
5. Decreasing volatility approaches 0.0.

Interpretation Guide

ATRN Value	Meaning	Trading Implications
0.9 - 1.0	Volatility at recent high	Extreme conditions; expand stops/targets
0.7 - 0.9	Above average volatility	Trending or volatile market
0.4 - 0.6	Average volatility	Normal conditions
0.2 - 0.4	Below average volatility	Consolidation; potential breakout setup
0.0 - 0.2	Volatility at recent low	Extreme quiet; mean reversion likely

Common Pitfalls

• Scale Independence: ATRN is relative to the asset's own history. An ATRN of 0.8 on AAPL is not comparable to 0.8 on BTC—they're measuring different things.

• Lookback Sensitivity: The 10×period lookback window defines "recent history." Shorter lookbacks react faster but may produce whipsaw signals. The default balances responsiveness and stability.

• Lag: Like all smoothed indicators, ATRN lags the actual volatility state. By the time ATRN hits 1.0, the volatility spike may already be fading.

• Not a Directional Indicator: ATRN measures the magnitude of volatility, not its direction. High ATRN can occur in both rallies and crashes.

Use Cases

1. Position Sizing: Scale position size inversely with ATRN—smaller positions when ATRN is high, larger when low.

2. Stop Loss Adaptation: Tighter stops when ATRN is low (quiet market), wider stops when ATRN is high (volatile market).

3. Regime Detection: Use ATRN thresholds to switch between mean-reversion (low ATRN) and trend-following (high ATRN) strategies.

4. Volatility Breakout: Look for moves from ATRN < 0.2 to ATRN > 0.5 as potential breakout confirmation.