Project Overview
Traditional volatility indicators like VIX treat each data point independently. But market stress rarely manifests in just one dimension—during COVID crash (March 2020), we saw simultaneous spikes in volatility, unusual volume, and correlation breakdowns.
This is probabilistic anomaly detection—we measure how "unlikely" each day's observation is under the learned distribution.
Statistical Methodology
Feature Engineering
Four features capture market dynamics:
- Log Return
- Rolling σ (14d)
- Volume Δ
- |Return|
Multivariate Gaussian
Market state modeled as:
xt ~ N(μ̂t, Σ̂t)
Parameters estimated via Maximum Likelihood from trailing 60 trading days. Regularization (εI) ensures positive definiteness.
Mahalanobis Distance
Anomaly score via generalized distance:
D² = (x-μ)ᵀ Σ⁻¹ (x-μ)
Under H₀, D² ~ χ²(4). This provides a principled threshold framework.
Detection Criterion
Anomaly flagged when:
D²t > Q0.995(D²)
Percentile-based threshold is robust to fat tails in return distributions.