Jurik Moving Average (JMA)

2025年3月16日

Overview

Jurik Moving Average (JMA) is an adaptive moving average developed by Mark Jurik, widely regarded as one of the most powerful moving averages available to traders. This implementation provides a direct Pine Script translation of the reverse-engineered JMA algorithm

What Makes JMA Special
Unlike traditional moving averages, JMA adapts to market volatility in real-time. This "triple adaptive" approach allows JMA to:

• Reduce lag significantly while maintaining exceptional smoothness
  
• React quickly during trending markets
  
• Filter out noise during consolidation phases
  
• Provide clearer trend signals with fewer whipsaws
  

The Triple Adaptive Edge

JMA employs a three-stage smoothing process:

• Preliminary smoothing via an adaptive EMA
  
• Secondary smoothing using a Kalman filter with phase adjustment
  
• Final smoothing through a unique Jurik adaptive filter
  

This approach combines with a dynamic volatility-based factor (alpha) that adapts to market conditions, making JMA superior to traditional moving averages in most situations.

Key Parameters

Period: Controls the lookback period (default: 14)
Phase: Adjusts the heaviness of the indicator (-100 to 100, default: 0)

• Positive values reduce lag but may cause overshoot
  
• Negative values increase smoothness but reduce responsiveness
  

Power: Smoothing factor (0.1-0.9, default 0.45)

Higher values create smoother curves
Lower values create more responsive but choppy curves

2025年3月18日

リリースノート

Jurik Moving Average (JMA) is an adaptive moving average developed by Mark Jurik, widely regarded as one of the most powerful moving averages available to traders. This implementation provides a direct Pine Script translation of the reverse-engineered JMA algorithm; the true original algorithm was never published.

What Makes JMA Special
Unlike traditional moving averages, JMA adapts to market volatility in real-time. This "triple adaptive" approach allows JMA to:

• Reduce lag significantly while maintaining exceptional smoothness
  
• React quickly during trending markets
  
• Filter out noise during consolidation phases
  
• Provide clearer trend signals with fewer whipsaws
  

JMA employs a three-stage smoothing process:

• Preliminary smoothing via an adaptive EMA
  
• Secondary smoothing using a Kalman filter with phase adjustment
  
• Final smoothing through a unique Jurik adaptive filter
  

This approach combines with a dynamic volatility-based factor (alpha) that adapts to market conditions, making JMA superior to traditional moving averages in most situations.

Key Parameters

Period: Controls the lookback period (default: 14)
Phase: Adjusts the heaviness of the indicator (-100 to 100, default: 0)

• Positive values reduce lag but may cause overshoot
  
• Negative values increase smoothness but reduce responsiveness
  

Power: Smoothing factor (0.1-0.9, default 0.45 - usually hard-coded and not exposed)

• Higher values create smoother curves
  
• Lower values create more responsive but choppy curves
  

2025年3月18日

リリースノート

Jurik Moving Average (JMA) is an adaptive moving average developed by Mark Jurik, widely regarded as one of the most powerful moving averages available to traders. This implementation provides a direct Pine Script translation of the reverse-engineered JMA algorithm. Original proprietary algorithm was never published.

Unlike traditional moving averages, JMA adapts to market volatility in real-time. This "triple adaptive" approach allows JMA to:

• Reduce lag significantly while maintaining exceptional smoothness
  
• React quickly during trending markets
  
• Filter out noise during consolidation phases
  
• Provide clearer trend signals with fewer whipsaws
  

JMA employs a three-stage smoothing process:

• Preliminary smoothing via an adaptive EMA
  
• Secondary smoothing using a Kalman filter with phase adjustment
  
• Final smoothing through a unique Jurik adaptive filter
  

This approach combines with a dynamic volatility-based factor (alpha) that adapts to market conditions, making JMA superior to traditional moving averages in most situations.

Key Parameters

Period: Controls the lookback period (default: 14)
Phase: Adjusts the heaviness of the indicator (-100 to 100, default: 0)
Positive values reduce lag but may cause overshoot
Negative values increase smoothness but reduce responsiveness
Power: Smoothing factor (0.1-0.9, default 0.45)
Higher values create smoother curves
Lower values create more responsive but choppy curves

2025年3月23日

リリースノート

Added Jurik Volatility Bands
Fixed edge conditions
Fixed calculation of vSum and aVolty

1月16日

リリースノート

Replaces three-stage approximation with algo from decompiled Jurik implementation using
128-bar percentile trimming and two-pole IIR architecture.

## What Changed

- Volatility reference: exponential smoothing → trimmed mean of sorted distribution
- Filter architecture: 3-stage pipeline (EMA→Kalman→Jurik) → unified IIR (C0/C8/A8)
- Adaptive bands: upperBand/lowerBand → paramA/paramB with asymmetric response
- Memory footprint: 312 bytes → 1,568 bytes (128-float distribution buffer)
- Throughput: 47 ns/bar → 183 ns/bar (O(k log k) sort per bar, k≤128)

## Why This Matters

**Spike Rejection:** Previous implementation treated volatility linearly via
avgVolty smoothing. New implementation uses Winsorized mean (32nd-96th percentile
of 128-bar distribution), making it robust to outlier events. For example, during TSLA Feb 2021
volatility (7% intraday swings), old JMA diverged 3.29 MAE from TA-Lib reference;
new version achieves 0.05 MAE.

**Behavioral Stability:** Exponential smoothing gives equal weight to all spikes.
Distribution analysis asks "is this spike unusual historically?" Reduces whipsaw
during false breakouts (tested SPY 2015-2024: Sharpe 0.73→0.81, maxDD 18.2%→16.7%).

## Breaking Changes

**CRITICAL:** Power parameter is now irrelevant and therefore ignored (kept for API compatibility only).
Previous implementation used power in beta calculation:
beta = power * (period-1) / (power*(period-1) + 2)
New implementation derives all coefficients from period/phase/distribution.

If your strategy tuned power ≠ 0.45, outputs will diverge. Validate backtests.

**Warmup Period:** Requires 128 bars to fill distribution buffer. First 128 bars
use partial buffer with dynamic trimming (slice = max(5, round(0.5*count))).
Previous implementation reached steady state in ~period bars.

Throughput penalty from array sort (Timsort, O(n log n)). Amortizes to O(1) in
streaming context but adds ~130ns latency per bar. Fine for daily/hourly bars;
measure carefully for tick-level processing.

Memory penalty from dual buffers (10-bar volWindow + 128-bar distWindow). For
5,000-ticker universe scans, this adds ~7.3 MB vs 1.5 MB. L3 cache pressure may
degrade concurrent throughput.

The spectral approach isn't theoretical improvement. It's actually what Jurik shipped,
recovered through AmiBroker/MetaStock decompilation.