QuanTAlib/lib/dynamics/chop/Chop.md

CHOP: Choppiness Index

Choppiness index quantifies how range-bound a market is — high values mean sideways, low values mean trending.

Property	Value
Category	Dynamic
Inputs	OHLCV bar (TBar)
Parameters	period (default 14)
Outputs	Single series (CHOP)
Output range	Varies (see docs)
Warmup	period bars
PineScript	chop.pine

• The Choppiness Index is a non-directional regime indicator that measures whether the market is trending or trading sideways.
• Similar: ADX, VHF | Complementary: BBands for range boundaries | Trading note: Choppiness Index; high values = choppy/ranging, low values = trending. Range 0–100.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

The Choppiness Index is a non-directional regime indicator that measures whether the market is trending or trading sideways. It compares total price movement (sum of True Range) to net price movement (high-low channel width) using a logarithmic ratio, producing a bounded value where high readings indicate choppy/consolidating conditions and low readings indicate trending conditions. CHOP does not indicate direction — only whether directional strategies are likely to succeed. The logarithmic scaling normalizes the output to approximately 0-100 regardless of price level or volatility magnitude.

Historical Context

Australian commodity trader E.W. Dreiss created the Choppiness Index to help traders avoid whipsaw losses by identifying market conditions unsuitable for trend-following strategies. The core insight is geometric: in a perfect trend, total bar-by-bar movement (sum of True Range) roughly equals the net distance traveled (channel width). In a choppy market, total movement greatly exceeds net progress — the market thrashes back and forth, accumulating True Range while the net channel stays narrow. The ratio between these two quantities, log-scaled to normalize across instruments and timeframes, produces a clean regime classifier. The conventional thresholds (38.2 and 61.8) are deliberately chosen as Fibonacci levels, though their efficacy is empirical rather than mathematical.

Architecture & Physics

1. True Range Accumulation

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

A rolling sum maintains \sum_{i=1}^{N} TR_i over the lookback window.

2. Price Channel Width

The net price movement over the same window:

\text{Channel} = \max(H_{t-N+1:t}) - \min(L_{t-N+1:t})

3. Choppiness Index

\text{CHOP} = 100 \times \frac{\log_{10}\!\left(\dfrac{\sum TR_N}{\text{Channel}}\right)}{\log_{10}(N)}

The denominator \log_{10}(N) normalizes the output so that the theoretical maximum approaches 100 (when \sum TR = N \times \text{Channel}, which occurs when every bar traverses the full channel).

4. Complexity

• Time: O(N) per bar for min/max scanning of high/low buffers; rolling sum is O(1)
• Space: O(N) — three ring buffers (TR, highs, lows)
• Warmup: N bars

Mathematical Foundation

Parameters

Symbol	Parameter	Default	Constraint
N	period	14	N \geq 2

Interpretation

CHOP Value	Market Regime	Strategy Implication
> 61.8	High choppiness	Avoid trend-following; favor range strategies
38.2 - 61.8	Ambiguous	Mixed conditions; reduced position sizing
< 38.2	Low choppiness	Market trending; favor momentum/breakout strategies

Geometric Intuition

• Perfect trend (straight line): \sum TR \approx \text{Channel}, so \log_{10}(1) = 0, CHOP \to 0
• Maximum chop (full traversal every bar): \sum TR \approx N \times \text{Channel}, so \log_{10}(N) / \log_{10}(N) = 1, CHOP \to 100

Non-Directional Property

CHOP is completely direction-agnostic. A strong uptrend and a strong downtrend produce identical low CHOP readings. Direction must be determined by a separate indicator (AMAT, ADX directional components, or simple price comparison).

Performance Profile

Operation Count (Streaming Mode)

CHOP needs True Range sum over N bars (running sum from RingBuffer) and ATR-N (highest high minus lowest low over N bars).

Post-warmup steady state (per bar):

Operation	Count	Cost (cycles)	Subtotal
TR computation (SUB×3, ABS×2, MAX×2)	7	1	7
RingBuffer write + oldest sub (TR sum)	2	1	2
Deque update × 2 (high/low window extrema)	4	1	4
SUB (highest_high − lowest_low = range)	1	1	1
DIV (TR_sum / range)	1	15	15
LOG10 (normalize to period)	1	20	20
DIV (scale by log10(N))	1	15	15
MUL (scale to 100)	1	3	3
Total	18	—	~67 cycles

For default N=14: ~67 cycles per bar. The LOG10 call is the dominant cost.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
TR computation	Yes	VSUBPD + VABSPD + VMAXPD per bar
Prefix-sum TR	Partial	Inclusive prefix sum with SIMD subtract-lag
Sliding high/low extrema	Partial	Lemire deque or sparse table; ArgMax/ArgMin scan
LOG10 + scaling	Yes	SVML vlog10 or Taylor approx; scalar fallback

With AVX2 and Intel SVML for vectorized log, batch mode achieves ~3× throughput for large datasets.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	LOG10 precision sufficient; FMA could be applied to TR computation
Timeliness	6/10	N-bar lookback; instantaneous response to volatility regime changes
Smoothness	5/10	Raw ratio is noisy; often used with EMA smoothing externally
Noise Rejection	6/10	Logarithmic scaling reduces extreme value sensitivity

Resources

• Dreiss, E.W. — Choppiness Index (original development)
• PineScript reference: chop.pine in indicator directory