Miha Kralj
90d5638008
- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
4.2 KiB
CHOP: Choppiness Index
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 isO(1) - Space:
O(N)— three ring buffers (TR, highs, lows) - Warmup:
Nbars
Mathematical Foundation
Parameters
| Symbol | Parameter | Default | Constraint |
|---|---|---|---|
N |
period | 14 | N \geq 2 |
Pseudo-code
Initialize:
trBuf = RingBuffer(period)
highBuf = RingBuffer(period)
lowBuf = RingBuffer(period)
trSum = 0
prevClose = NaN
logPeriod = log10(period)
On each bar (high, low, close, isNew):
if !isNew: restore previous state
// True Range
if prevClose is valid:
TR = max(high - low, |high - prevClose|, |low - prevClose|)
else:
TR = high - low
// Rolling sum update
if trBuf is full:
trSum -= trBuf.Oldest
trBuf.Add(TR)
trSum += TR
highBuf.Add(high)
lowBuf.Add(low)
// Channel width
maxHigh = Max(highBuf)
minLow = Min(lowBuf)
channel = maxHigh - minLow
// Choppiness Index
if channel > 0 AND trSum > 0:
CHOP = 100 × log10(trSum / channel) / logPeriod
else:
CHOP = 50 // neutral fallback
prevClose = close
output = Clamp(CHOP, 0, 100)
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).
Resources
- Dreiss, E.W. — Choppiness Index (original development)
- PineScript reference:
chop.pinein indicator directory