Statistical Methods

Overview

This section outlines the statistical methodologies and quantitative techniques employed across research projects.

Time Series Analysis

Autocorrelation and Persistence

• Ljung-Box Test: Testing for serial correlation
• Augmented Dickey-Fuller: Stationarity testing
• Half-life Estimation: Mean reversion speed measurement

Volatility Modeling

• Realized Volatility: High-frequency volatility estimation
• GARCH Models: Conditional heteroskedasticity
• Regime Switching: Multiple volatility states

Microstructure Analysis

Order Flow Metrics

• Information Coefficient: Predictive power measurement
• T-Statistics: Statistical significance testing
• Cross-correlation: Lead-lag relationships

VWAP Analysis

• Mean Reversion Testing: Price anchoring effects
• Autocorrelation Functions: Persistence measurement
• Distance Metrics: Deviation quantification

Machine Learning Methods

Dimensionality Reduction

• Principal Component Analysis (PCA): Feature extraction
• Explained Variance: Component selection criteria

Clustering

• K-means: Regime identification
• Silhouette Analysis: Optimal cluster selection
• Cluster Validation: Within/between cluster variance

Statistical Testing

Hypothesis Testing

• Two-tailed t-tests: Mean difference testing
• Bonferroni Correction: Multiple testing adjustment
• Bootstrap Methods: Confidence interval estimation

Performance Metrics

• Sharpe Ratio: Risk-adjusted returns
• Information Ratio: Active return per unit risk
• Maximum Drawdown: Worst-case loss measurement

Risk Management

Value at Risk (VaR)

• Historical Simulation: Empirical risk estimation
• Parametric Methods: Normal and t-distribution assumptions
• Expected Shortfall: Tail risk measurement

Correlation Analysis

• Pearson Correlation: Linear relationships
• Spearman Rank: Non-parametric correlation
• Rolling Correlations: Time-varying relationships