Self-Organized Criticality - Avalanche DistributionHere's all you need to know: This indicator applies Self-Organized Criticality (SOC) theory to financial markets, measuring the power-law exponent (alpha) of price drawdown distributions. It identifies whether markets are in stable Gaussian regimes or critical states where large cascading moves become more probable.
Self-Organized Criticality
SOC theory, introduced by Per Bak, Tang, and Wiesenfeld (1987), describes how complex systems naturally evolve toward critical (fragile) states. An example is a sand pile: adding grains creates avalanches whose sizes follow a power-law distribution rather than a normal distribution.
Financial markets exhibit similar behavior. Price movements aren't purely random walks—they display:
Fat-tailed distributions (more extreme events than Gaussian models predict)
Scale invariance (no characteristic avalanche size)
Intermittent dynamics (periods of calm punctuated by large cascades)
Power-Law Distributions
When a system is in a critical state, the probability of an avalanche of size s follows:
P(s) ∝ s^(-α)
Where:
α (alpha) is the power-law exponent
Higher α → distribution resembles Gaussian (large events rare)
Lower α → heavy tails dominate (large events common)
This indicator estimates α from the empirical distribution of price drawdowns.
Mathematical Method
1. Avalanche Detection
The indicator identifies local price peaks (highest point in a lookback window), then measures the percentage drawdown to the next trough. A dynamic ATR-based threshold filters out noise—small drops in calm markets count, but the bar rises in volatile periods.
2. Logarithmic Binning
Avalanche sizes are sorted into logarithmically-spaced bins (e.g., 1-2%, 2-4%, 4-8%) rather than linear bins. This captures power-law behavior across multiple scales - a 2% drop and 20% crash both matter. The indicator creates 12 adaptive bins spanning from your smallest to largest observed avalanche.
3. Bin-to-Bin Ratio Estimation
For each pair of adjacent bins, we calculate:
α ≈ log(N₁/N₂) / log(s₂/s₁)
Where N₁ and N₂ are avalanche counts, s₁ and s₂ are bin sizes.
Example: If 2% drops happen 4× more often than 4% drops, then α ≈ log(4)/log(2) ≈ 2.0.
We get 8-11 independent estimates and average them. This is more robust than fitting one line through all points—outliers can't dominate.
4. Rolling Window Analysis
Alpha recalculates using only recent avalanches (default: last 500 bars). Old data drops out as new avalanches occur, so the indicator tracks regime shifts in real-time.
Regime Classification
🟢 Gaussian α ≥ 2.8 Normal distribution behavior; large moves are rare outliers
🟡 Transitional 1.8 ≤ α < 2.8 Moderate fat tails; system approaching criticality
🟠 Critical 1.0 ≤ α < 1.8 Heavy tails; large avalanches increasingly common
🔴 Super-Critical α < 1.0 Extreme tail risk; system prone to cascading failures
What Alpha Tells You
Declining alpha → Market moving toward criticality; tail risk increasing
Rising alpha → Market stabilizing; returns to normal distribution
Persistent low alpha → Sustained fragility; heightened crash probability
Supporting Metrics
Heavy Tail %: Concentration of total drawdown in largest 10% of events
Populated Bins: Data coverage quality (11-12 out of 12 is ideal)
Avalanche Count: Sample size for statistical reliability
Limitations
This is a distributional measure, not a timing indicator. Low alpha indicates increased systemic risk but doesn't predict when a cascade will occur. Only that the probability distribution has shifted toward larger events.
How This Differs from the Per Bak Fragility Index
The SOC Avalanche Distribution calculates the power-law exponent (alpha) directly from price drawdown distributions - a pure mathematical analysis requiring only price data. The Per Bak Fragility Index aggregates external stress indicators (VIX, SKEW, credit spreads, put/call ratios) into a weighted composite score.
Technical Notes
Default settings optimized for daily and weekly timeframes on major indices
Requires minimum 200 bars of history for stable estimates
ATR-based dynamic sizing prevents scale-dependent bias
Alerts available for regime transitions and super-critical entry
References
Bak, P., Tang, C., & Wiesenfeld, K. (1987). Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters.
Sornette, D. (2003). Why Stock Markets Crash: Critical Events in Complex Financial Systems. Princeton University Press.
SELF
Self-Adjusting RSI +Here is an open source (no request needed!) version of the Self-Adjusting RSI by David Sepiashvili.
Published in Stocks & Commodities V. 24:2 (February, 2006): The Self-Adjusting RSI
David Sepiashvili's article, "The Self-Adjusting RSI," presents a technique to adjust the traditional RSI overbought and oversold thresholds so as to ensure that 70-80% of RSI values lie between the two thresholds. Sepiashvili presents two algorithms for adjusting the thresholds. One is based on standard deviation, the other on a simple moving average of the RSI.
This script allows you to choose between plotting the Self-Adjusting bands or the traditional bands. You can also plot a smoothed RSI (SMA or EMA) and change the theme color for dark or light charts.
If you find this code useful, please pass it forward by sharing open source!
Thank you to all of the open source heroes out there!
"If I have seen a little further it is by standing on the shoulders of Giants."
