Statistical Indicators

Master 58 advanced statistical indicators for quantitative analysis, risk assessment, and pattern detection

58 IndicatorsQuantitative AnalysisAdvanced Math

Why Statistical Indicators Matter

Statistical indicators bring mathematical rigor to trading decisions. Instead of relying on subjective technical analysis, these tools apply proven statistical methods to quantify relationships, measure risk, and identify patterns in market data.

  • ✓ Quantify risk and portfolio volatility scientifically
  • ✓ Detect correlations and comovement patterns
  • ✓ Identify mean reversion opportunities
  • ✓ Assess systematic vs unsystematic risk

These 58 indicators represent institutional-grade quantitative tools used in algorithmic trading, hedge funds, and systematic portfolios worldwide. They excel at removing emotion from trading decisions.

  • ✓ Performance metric calculation
  • ✓ Volatility and risk management
  • ✓ Pattern recognition and complexity analysis
  • ✓ Multi-asset portfolio construction

Showing 58 of 58 indicators

🔄
Correlation

Autocorrelation

Measures how current values correlate with lagged versions of themselves

Pattern Detection
📊
Risk

Beta

Measures systematic risk - how much an asset moves relative to the market

Risk Assessment
🔗
Correlation

Cointegration

Tests if two or more time series move together in long-term equilibrium

Relationship
📈
Correlation

Correlation

Measures linear relationship strength between two variables (-1 to 1)

Fundamental
⚠️
Risk

CVaR

Tail risk metric - expected loss in worst-case scenarios beyond VaR

Tail Risk
📉
Pattern

DFA

Analyzes long-range correlations and trends in non-stationary data

Advanced Analysis
🌀
Pattern

Fractal Dimension

Measures complexity and self-similarity of price movement patterns

Complexity
⏱️
Mean Reversion

Half-Life Mean Reversion

Measures how quickly prices revert to their mean

Reversion
📊
Trend

Hurst Exponent

Measures trending vs mean-reverting behavior (0.5 = random)

Regime
Performance

Information Ratio

Risk-adjusted return metric - excess return per unit of tracking error

Return Analysis
🔍
Smoothing

Kalman Filter

Smooths noisy data and predicts next value using recursive Bayesian estimation

Filtering
🌊
Pattern

Market Entropy

Measures information and disorder in price movements (high = random)

Entropy
🎯
Mean Reversion

Mean Reversion Score

Quantifies likelihood and speed of mean reversion (0-100 scale)

Composite
⚖️
Performance

Omega Ratio

Measures probability of gains above target vs losses below target

Return Analysis
📈
Performance

Rolling Alpha

Excess return over market (using CAPM) in rolling windows

Rolling Metric
🔮
Prediction

Rolling IC

Correlation between predicted and actual returns in rolling windows

Rolling Metric
📊
Risk

Rolling Kurtosis

Measures tail risk in rolling windows (high = fat tails)

Rolling Metric
📉
Risk

Rolling Max Drawdown

Maximum peak-to-trough decline in rolling windows

Rolling Metric
🔬
Analysis

Rolling PCA

Extracts main sources of variance from multiple correlated variables

Rolling Metric
Performance

Rolling Sharpe

Risk-adjusted returns in rolling windows (return per unit risk)

Rolling Metric
📊
Risk

Rolling Skewness

Measures asymmetry of return distribution in rolling windows

Rolling Metric
📐
Uncertainty

Rolling Standard Error

Uncertainty estimate of rolling mean in sliding windows

Rolling Metric
📈
Volatility

Rolling Variance

Volatility measure in rolling windows (variance of returns)

Rolling Metric
Performance

Treynor Ratio

Excess return per unit of systematic risk (Beta) - similar to Sharpe

Return Analysis
📊
Risk

VaR

Maximum expected loss at specified confidence level

Risk Quantification
📏
Normalization

Z-Score

Standardized score showing how many standard deviations from mean

Fundamental
🔄
Correlation

Autocorrelation Pass

Rolling autocorrelation of a series — measures how current values correlate with lagged versions

Pass
⚠️
Risk

CVaR Pass

Rolling Conditional Value at Risk — expected loss beyond the VaR threshold

Pass
📊
Performance

Calmar

Annualized return divided by maximum drawdown — aggregate risk-adjusted return ratio

Risk-Adjusted Return
🔗
Correlation

Cointegration Pass

Rolling cointegration test — detects long-term equilibrium relationships between series

Pass
📈
Correlation

Covariance

Rolling covariance between two series — measures joint variability

Relationship
📉
Pattern

DFA Pass

Detrended Fluctuation Analysis — measures long-range power-law correlations

Pass
📉
Risk

Drawdown

Per-bar drawdown from running peak — tracks decline from all-time high in window

Risk Measure
🌀
Pattern

Fractal Dimension Pass

Rolling fractal dimension — measures price complexity and market efficiency

Pass
⏱️
Mean Reversion

Half-Life Mean Reversion Pass

Rolling half-life of mean reversion — how quickly a series reverts to its mean

Pass
📊
Trend

Hurst Exponent Pass

Rolling Hurst exponent — distinguishes trending (H>0.5), random (H=0.5), mean-reverting (H<0.5)

Pass
Performance

Information Ratio Pass

Rolling information ratio — active return per unit of tracking error

Pass
🔍
Smoothing

Kalman Filter Pass

Kalman filter smoother — optimal recursive noise reduction with process and measurement noise params

Pass
📈
Returns

Log Return

Per-bar continuously compounded log return — ln(P[i]/P[i-1])

Returns
🌊
Pattern

Market Entropy Pass

Rolling Shannon entropy of binned price changes — measures market randomness

Pass
🎯
Mean Reversion

Mean Reversion Score Pass

Composite mean-reversion score combining multiple statistical signals

Pass
📏
Normalization

Min-Max Normalisation

Normalises values to [0, 1] range within a rolling window — (v−min)/(max−min)

Normalisation
⚖️
Performance

Omega Ratio Pass

Rolling Omega ratio — sum of gains above threshold divided by losses below threshold

Pass
🏆
Normalization

Rank

Percentile rank within rolling window — non-parametric normalisation [0, 100]

Normalisation
📈
Performance

Rolling Alpha Pass

Jensen's Alpha — excess return over CAPM-predicted return using rolling beta

Pass
🔮
Prediction

Rolling IC Pass

Rolling information coefficient — Spearman rank correlation between signal and forward return

Pass
📊
Risk

Rolling Kurtosis Pass

Rolling excess kurtosis — measures fat-tail risk within a sliding window

Pass
📉
Risk

Rolling Max Drawdown Pass

Worst peak-to-trough decline within a rolling window — output in [0, 1]

Pass
🔬
Analysis

Rolling PCA Pass

Rolling PCA score — first principal component extracted from a sliding window

Pass
Performance

Rolling Sharpe Pass

Rolling Sharpe ratio — mean excess return divided by standard deviation

Pass
📊
Risk

Rolling Skewness Pass

Rolling skewness — measures distribution asymmetry within a sliding window

Pass
📐
Uncertainty

Rolling Standard Error Pass

Rolling standard error of the mean — SE = σ / √n within a sliding window

Pass
📈
Volatility

Rolling Variance Pass

Rolling sample variance — Σ(x−μ)²/(n−1) within a sliding window

Pass
📈
Returns

Simple Return

Cumulative simple return from inception — (P[i] − P[0]) / P[0]

Returns
Performance

Treynor Ratio Pass

Rolling Treynor ratio — excess return per unit of systematic risk (beta)

Pass
📊
Risk

VaR Pass

Rolling historical Value at Risk — loss threshold exceeded with (1−confidence) probability

Pass
📏
Normalization

Z-Score Pass

Rolling Z-score — how many standard deviations the current value is from the rolling mean

Pass
🛡️
Normalization

Z-Score Robust

Outlier-resistant Z-score using median and MAD instead of mean and standard deviation

Normalisation

Browse by Category

Getting Started with Statistical Indicators

For Beginners

  1. 1. Learn Z-Score for standardization and normalization
  2. 2. Master Correlation for relationship analysis
  3. 3. Understand Beta for systematic risk assessment
  4. 4. Explore Rolling Sharpe for performance metrics

Pro Strategies

  • • Use Beta for systematic portfolio construction and hedging
  • • Combine Hurst Exponent with rolling metrics for regime detection
  • • Employ mean reversion indicators for pair trading strategies
  • • Leverage Monte Carlo VaR for comprehensive risk management