Z-Score & Stats

This is an advanced indicator that measures price deviation from its mean using statistical z-scores, combined with multiple analytical features for trading signals.

Core Functionality-
Z-Score Calculation Engine:
The indicator uses a custom standardization function that calculates how many standard deviations the current price is from its rolling mean. Unlike simple moving averages, this provides a normalized view of price extremes. The calculation maintains a sliding window of data points, efficiently updating mean and variance values as new data arrives while removing old data points. This approach handles missing values gracefully and uses sample variance (rather than population variance) for more accurate statistical measurements.

Statistical Zones & Visual Framework:
The indicator creates a visual representation of statistical probability zones:

±1 Standard Deviation: Encompasses about 68% of normal price behavior (green zone)
±2 Standard Deviations: Covers approximately 95% of price movements (orange zone)
±3 Standard Deviations: Represents 99.7% probability range (red zone)
±3.5 and ±4 Thresholds: Extreme outlier levels that trigger special alerts

The z-score line changes color dynamically based on which zone it occupies, making it easy to identify the current market extremity at a glance.

Advanced Features:
Volume Contraction Analysis
The script monitors volume patterns to identify periods of reduced trading activity. It compares current volume against a moving average and flags when volume drops below a specified threshold (default 70%). Volume contraction often precedes significant price moves and is factored into the optimal entry detection system.

Momentum-Based Direction Model:
Rather than just showing current z-score levels, the indicator projects where the z-score is likely to move based on recent momentum. It calculates the rate of change in the z-score and extrapolates forward for a specified number of bars. This creates a directional arrow that indicates whether conditions are bullish (negative z-score with upward momentum) or bearish (positive z-score with downward momentum).

Divergence Detection System:
The script automatically identifies four types of divergences between price action and z-score behavior :-
Regular Bullish Divergence: Price makes lower lows while z-score makes higher lows, suggesting weakening downward pressure
Regular Bearish Divergence: Price makes higher highs while z-score makes lower highs, indicating exhaustion in the uptrend
Hidden Bullish Divergence: Price makes higher lows while z-score makes lower lows, confirming trend continuation in an uptrend
Hidden Bearish Divergence: Price makes lower highs while z-score makes higher highs, confirming downtrend continuation
The system uses pivot detection with configurable lookback periods and distance requirements, then draws connecting lines and labels directly on the chart when divergences occur.

Yearly Statistics Tracking:
The indicator maintains historical records of maximum z-score deviations over yearly periods (configurable bar count). This provides context by showing whether current extremes are unusual compared to typical annual ranges. The average yearly maximum helps traders understand if the current market is exhibiting normal volatility or exceptional conditions.

Mean Reversion Probability:
Based on the current z-score magnitude, the indicator calculates and displays the statistical probability that price will revert toward the mean. Higher absolute z-scores indicate stronger mean reversion probabilities, ranging from 38% at ±0.5 standard deviations to 99.7% at ±3 standard deviations.

Comprehensive Statistics Table:
A customizable on-chart table displays real-time statistics including:

Current z-score value with directional indicator
Predicted z-score based on momentum
Current year's maximum absolute z-score
Historical average yearly maximum
Mean reversion probability percentage
Zone status classification (Normal, Moderate, High, Extreme)
Directional bias (Bullish, Bearish, Neutral)
Active divergence status
Volume contraction status with ratio
Optimal setup detection (combining extreme z-scores with volume contraction)

Optimal Entry Setup Detection:
The most sophisticated feature identifies high-probability trading setups by combining multiple factors. An "Optimal Long" signal triggers when z-score reaches -3.5 or below AND volume is contracted. An "Optimal Short" signal appears when z-score exceeds +3.5 AND volume is contracted. This combination suggests extreme price deviation occurring on low volume, often preceding strong reversals.

Alert System:
The script includes a unified alert mechanism that triggers when z-score crosses specific thresholds:
Crossing above/below ±3.5 standard deviations (extreme levels)
Crossing above/below ±4 standard deviations (critical levels)
Alerts fire once per bar with confirmation (previous bar must be on opposite side of threshold) to avoid false signals.

Practical Application:
This indicator is designed for mean reversion traders who seek statistically significant price extremes. The combination of z-score measurement, volume analysis, momentum projection, and divergence detection creates a multi-layered confirmation system. Traders can use extreme z-scores as potential reversal zones, while the direction model and divergence signals help time entries more precisely. The volume contraction filter adds an additional layer of confluence, identifying moments when reduced participation may precede explosive moves back toward the mean.

Chart Attached: NSE GMR Airports, EoD 12/12/25

DISCLAIMER: This information is provided for educational purposes only and should not be considered financial, investment, or trading advice.Happy Trading