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Miha Kralj
121 lines
6.2 KiB
Markdown
121 lines
6.2 KiB
Markdown
# CHOP: Choppiness Index
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> *Choppiness index quantifies how range-bound a market is — high values mean sideways, low values mean trending.*
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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` (default 14) |
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| **Outputs** | Single series (CHOP) |
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| **Output range** | Varies (see docs) |
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| **Warmup** | `period` bars |
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| **PineScript** | [chop.pine](chop.pine) |
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- The Choppiness Index is a non-directional regime indicator that measures whether the market is trending or trading sideways.
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- **Similar:** [ADX](../adx/Adx.md), [VHF](../vhf/Vhf.md) | **Complementary:** BBands for range boundaries | **Trading note:** Choppiness Index; high values = choppy/ranging, low values = trending. Range 0–100.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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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.
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## Historical Context
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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.
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## Architecture & Physics
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### 1. True Range Accumulation
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$$TR_t = \max(H_t - L_t,\; |H_t - C_{t-1}|,\; |L_t - C_{t-1}|)$$
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A rolling sum maintains $\sum_{i=1}^{N} TR_i$ over the lookback window.
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### 2. Price Channel Width
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The net price movement over the same window:
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$$\text{Channel} = \max(H_{t-N+1:t}) - \min(L_{t-N+1:t})$$
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### 3. Choppiness Index
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$$\text{CHOP} = 100 \times \frac{\log_{10}\!\left(\dfrac{\sum TR_N}{\text{Channel}}\right)}{\log_{10}(N)}$$
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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).
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### 4. Complexity
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- **Time:** $O(N)$ per bar for min/max scanning of high/low buffers; rolling sum is $O(1)$
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- **Space:** $O(N)$ — three ring buffers (TR, highs, lows)
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- **Warmup:** $N$ bars
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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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### Interpretation
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| CHOP Value | Market Regime | Strategy Implication |
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|------------|---------------|---------------------|
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| > 61.8 | High choppiness | Avoid trend-following; favor range strategies |
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| 38.2 - 61.8 | Ambiguous | Mixed conditions; reduced position sizing |
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| < 38.2 | Low choppiness | Market trending; favor momentum/breakout strategies |
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### Geometric Intuition
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- **Perfect trend (straight line):** $\sum TR \approx \text{Channel}$, so $\log_{10}(1) = 0$, CHOP $\to 0$
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- **Maximum chop (full traversal every bar):** $\sum TR \approx N \times \text{Channel}$, so $\log_{10}(N) / \log_{10}(N) = 1$, CHOP $\to 100$
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### Non-Directional Property
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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).
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## Performance Profile
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### Operation Count (Streaming Mode)
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CHOP needs True Range sum over N bars (running sum from RingBuffer) and ATR-N (highest high minus lowest low over N bars).
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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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| TR computation (SUB×3, ABS×2, MAX×2) | 7 | 1 | 7 |
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| RingBuffer write + oldest sub (TR sum) | 2 | 1 | 2 |
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| Deque update × 2 (high/low window extrema) | 4 | 1 | 4 |
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| SUB (highest_high − lowest_low = range) | 1 | 1 | 1 |
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| DIV (TR_sum / range) | 1 | 15 | 15 |
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| LOG10 (normalize to period) | 1 | 20 | 20 |
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| DIV (scale by log10(N)) | 1 | 15 | 15 |
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| MUL (scale to 100) | 1 | 3 | 3 |
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| **Total** | **18** | — | **~67 cycles** |
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For default $N=14$: ~67 cycles per bar. The LOG10 call is the dominant cost.
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### Batch Mode (SIMD Analysis)
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| Operation | Vectorizable? | Notes |
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| :--- | :---: | :--- |
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| TR computation | Yes | VSUBPD + VABSPD + VMAXPD per bar |
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| Prefix-sum TR | Partial | Inclusive prefix sum with SIMD subtract-lag |
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| Sliding high/low extrema | Partial | Lemire deque or sparse table; ArgMax/ArgMin scan |
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| LOG10 + scaling | Yes | SVML vlog10 or Taylor approx; scalar fallback |
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With AVX2 and Intel SVML for vectorized log, batch mode achieves ~3× throughput for large datasets.
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 9/10 | LOG10 precision sufficient; FMA could be applied to TR computation |
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| **Timeliness** | 6/10 | N-bar lookback; instantaneous response to volatility regime changes |
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| **Smoothness** | 5/10 | Raw ratio is noisy; often used with EMA smoothing externally |
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| **Noise Rejection** | 6/10 | Logarithmic scaling reduces extreme value sensitivity |
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## Resources
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- Dreiss, E.W. — Choppiness Index (original development)
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- PineScript reference: `chop.pine` in indicator directory |