Statistical Indicators
Master 58 advanced statistical indicators for quantitative analysis, risk assessment, and pattern detection
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
Autocorrelation
Measures how current values correlate with lagged versions of themselves
Beta
Measures systematic risk - how much an asset moves relative to the market
Cointegration
Tests if two or more time series move together in long-term equilibrium
Correlation
Measures linear relationship strength between two variables (-1 to 1)
CVaR
Tail risk metric - expected loss in worst-case scenarios beyond VaR
DFA
Analyzes long-range correlations and trends in non-stationary data
Fractal Dimension
Measures complexity and self-similarity of price movement patterns
Half-Life Mean Reversion
Measures how quickly prices revert to their mean
Hurst Exponent
Measures trending vs mean-reverting behavior (0.5 = random)
Information Ratio
Risk-adjusted return metric - excess return per unit of tracking error
Kalman Filter
Smooths noisy data and predicts next value using recursive Bayesian estimation
Market Entropy
Measures information and disorder in price movements (high = random)
Mean Reversion Score
Quantifies likelihood and speed of mean reversion (0-100 scale)
Omega Ratio
Measures probability of gains above target vs losses below target
Rolling Alpha
Excess return over market (using CAPM) in rolling windows
Rolling IC
Correlation between predicted and actual returns in rolling windows
Rolling Kurtosis
Measures tail risk in rolling windows (high = fat tails)
Rolling Max Drawdown
Maximum peak-to-trough decline in rolling windows
Rolling PCA
Extracts main sources of variance from multiple correlated variables
Rolling Sharpe
Risk-adjusted returns in rolling windows (return per unit risk)
Rolling Skewness
Measures asymmetry of return distribution in rolling windows
Rolling Standard Error
Uncertainty estimate of rolling mean in sliding windows
Rolling Variance
Volatility measure in rolling windows (variance of returns)
Treynor Ratio
Excess return per unit of systematic risk (Beta) - similar to Sharpe
VaR
Maximum expected loss at specified confidence level
Z-Score
Standardized score showing how many standard deviations from mean
Autocorrelation Pass
Rolling autocorrelation of a series — measures how current values correlate with lagged versions
CVaR Pass
Rolling Conditional Value at Risk — expected loss beyond the VaR threshold
Calmar
Annualized return divided by maximum drawdown — aggregate risk-adjusted return ratio
Cointegration Pass
Rolling cointegration test — detects long-term equilibrium relationships between series
Covariance
Rolling covariance between two series — measures joint variability
DFA Pass
Detrended Fluctuation Analysis — measures long-range power-law correlations
Drawdown
Per-bar drawdown from running peak — tracks decline from all-time high in window
Fractal Dimension Pass
Rolling fractal dimension — measures price complexity and market efficiency
Half-Life Mean Reversion Pass
Rolling half-life of mean reversion — how quickly a series reverts to its mean
Hurst Exponent Pass
Rolling Hurst exponent — distinguishes trending (H>0.5), random (H=0.5), mean-reverting (H<0.5)
Information Ratio Pass
Rolling information ratio — active return per unit of tracking error
Kalman Filter Pass
Kalman filter smoother — optimal recursive noise reduction with process and measurement noise params
Log Return
Per-bar continuously compounded log return — ln(P[i]/P[i-1])
Market Entropy Pass
Rolling Shannon entropy of binned price changes — measures market randomness
Mean Reversion Score Pass
Composite mean-reversion score combining multiple statistical signals
Min-Max Normalisation
Normalises values to [0, 1] range within a rolling window — (v−min)/(max−min)
Omega Ratio Pass
Rolling Omega ratio — sum of gains above threshold divided by losses below threshold
Rank
Percentile rank within rolling window — non-parametric normalisation [0, 100]
Rolling Alpha Pass
Jensen's Alpha — excess return over CAPM-predicted return using rolling beta
Rolling IC Pass
Rolling information coefficient — Spearman rank correlation between signal and forward return
Rolling Kurtosis Pass
Rolling excess kurtosis — measures fat-tail risk within a sliding window
Rolling Max Drawdown Pass
Worst peak-to-trough decline within a rolling window — output in [0, 1]
Rolling PCA Pass
Rolling PCA score — first principal component extracted from a sliding window
Rolling Sharpe Pass
Rolling Sharpe ratio — mean excess return divided by standard deviation
Rolling Skewness Pass
Rolling skewness — measures distribution asymmetry within a sliding window
Rolling Standard Error Pass
Rolling standard error of the mean — SE = σ / √n within a sliding window
Rolling Variance Pass
Rolling sample variance — Σ(x−μ)²/(n−1) within a sliding window
Simple Return
Cumulative simple return from inception — (P[i] − P[0]) / P[0]
Treynor Ratio Pass
Rolling Treynor ratio — excess return per unit of systematic risk (beta)
VaR Pass
Rolling historical Value at Risk — loss threshold exceeded with (1−confidence) probability
Z-Score Pass
Rolling Z-score — how many standard deviations the current value is from the rolling mean
Z-Score Robust
Outlier-resistant Z-score using median and MAD instead of mean and standard deviation
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Getting Started with Statistical Indicators
For Beginners
- 1. Learn Z-Score for standardization and normalization
- 2. Master Correlation for relationship analysis
- 3. Understand Beta for systematic risk assessment
- 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